When was the last time the Republican nominee was arguably more left-leaning than the Democratic one

[Southern Senator North Carolina Yankee]

Plausibly 1888 or 1892. Harrison passed moderate anti-trust and silver legislation, as well as a generous pension for Civil War veterans, some internal improvements and a bill protecting national forests. Also tried to pass several civil rights measures like federal supervision of House elections in the South and funding for black public schools. Cleveand was a laissez faire pro-gold Bourbon Democrat who attacked Harrison's "Billion Dollar Congress" for its tax-and-spend initiatives.

Now it's not that quite clear cut when you consider that Harrison's tariff policy was pretty regressive and he was also heavily anti-immigration, as Republicans traditionally were. But business elites generally supported Cleveland in 1892 as a return to "sound money" after the flirting with bimetallism had exacerbated the Panic of 1890:

Regardless, the business press celebrated Harrison’s downfall. “Financial circles feel new hope,” declared the Commercial and Financial Chronicle. For despite the threat of low-tariff Democrats taking power, bankers and businessmen celebrated “the name and character of ex-President Cleveland…for the sound financial views he holds and for the adoption of those views by the convention that nominated him.” In fact, the Wall Street Journal observed that “so many good Republicans…voted for the Democratic party because they believe in Mr. Cleveland’s modified protective ideas”. Even the manufacturing community seemed relieved. “The [electoral] reaction against the present tariff, strangely enough, was not so pronounced in agricultural communities as in manufacturing localities” observed Iron Age, which assured readers that Cleveland would block any radical changes to protection. Instead, Cleveland would restore order to America’s finances. If only the economy could hold out until spring “for the assurance which conservative legislation alone can impart

I don't know when was the last presidential election in which the financial press backed the Democratic candidate, but it might be this one.

https://talkelections.org/FORUM/index.php?topic=371825.msg7331913#msg7331913

Also this:
https://www.livescience.com/34241-democratic-republican-parties-switch-platforms.html

From a business perspective, Rauchway pointed out, the loyalties of the parties did not really switch. "Although the rhetoric and to a degree the policies of the parties do switch places," he wrote, "their core supporters don't — which is to say, the Republicans remain, throughout, the party of bigger businesses; it's just that in the earlier era bigger businesses want bigger government and in the later era they don't."

In other words, earlier on, businesses needed things that only a bigger government could provide, such as infrastructure development, a currency and tariffs. Once these things were in place, a small, hands-off government became better for business.

That said there was an affirmative desire to compromise on currency and regulation under Harrison, the rest of his policies were the same "conservative" pro-business agenda the Whigs had supported and Harrison was the last ex-Whig to be President.

[Southern Senator North Carolina Yankee]

I would say 1948. Dewey seemed to be more left-leaning than Truman in my opinion. As a matter of fact, as a Republican, I probably would have voted for the latter.

I mean, ONLY in some vague “culturally conservative” vs. “culturally liberal” way, which is not only not a great barometer for 1940s politics but also only a small part of this equation.  Dewey pretty clearly ran to Truman’s right.

More accurately Truman ran to Dewey's left while Dewey spoke in platitudes. Truman saw himself as the spiritual heir to WJB and he therefore viewed himself as fighting for the common man against the "special privilege people" as he described it. Dewey meanwhile had close ties to Wall Street and while he had a moderate record as Governor, he did not emphasize it and instead allowed the Republican Party to be defined by the much more Conservative Congress, which Truman aggressively assailed on the campaign trail. 1948 is very much like 2012 in a sense, with a Midwest Democrat running against a Northeast establishment Republican, with the Taft-Hartley situation (Congress overriding Truman's veto painting him as the champion of the working class) in place of the Auto bailout (and its damaging effects on Romney and painting Obama as the savior of the Auto industry).

There is also the dynamic caused by Truman's desegregation of the military and the adopted of Humphrey's Civil Rights planks at the DNC. Because Truman let the Conservative wing of the Southern Democrats go and instead doubled down on the populist/Progressive wing (aided by his own heritage from the border states), Truman was helped to minimize losses in the South and at the same time score huge wins with black voters.

The combination of strong union support, black support and populisty up country Southern whites would deliver Truman back to the Presidency. The only candidate Truman ran to the right of in this election, was Henry Wallace.

[Southern Senator North Carolina Yankee]

1956

Exceptionally bad take.  Even if you insist on putting civil rights on a left/right scale as you clearly do, there are a plethora of other issues to consider.

This is clearly the only reasonable way to view the issue. The real question is why you are so insistent on putting 19th century issues of religion/morality on a 21st century spectrum.

Stop trying to make Protestant supremacism seem woke. It's not woke.

1892, 1904, and 1924 are all defensible answers to this question. 1904 is probably the best one. 1952, 1956, 1912, and especially 1948 and 1976 are all terrible answers, with 1912 as probably the best of a bad lot.

That 1924 is a possible answer really speaks to just how conservative John Davis was, rather than any progressivism on Silent Cal’s part. Although, I suppose the latter did have a surprisingly liberal attitude on civil rights (not just towards African Americans, but also Native Americans in particular).

Coolidge was actually regarded as leaning towards the progressive wing of the Republican Party whilst he was active in Massachusetts state politics (he supported women’s suffrage, laws to cut working hours for women and children and veterans bonuses). On the other hand, he seems to have not regarded it as the proper role of the federal government to be a driver of social reform, nor for the Presidency in and of itself to be ‘activist’. However, it’s arguable that the conservative financial policies that Coolidge is typically associated were in fact primarily driven by the Treasury Secretary Andrew Mellon rather than the President himself (it’s also worth noting that Herbert Hoover clashed with Mellon over the extent of his tax cutting proposals).

Coolidge's reputation in libertarian circles is largely overblown for the most part. A good part of it was a poor working relationship with congress and distant approach, in part because of his extremely reserved personality.

His administration presided over sky high tariffs, he signed a bill massively restricting immigration and regardless of his personal feelings on the matter, he was President during Prohibition.

If anything he comes across more as a conservative nationalist than some paragon of libertarianism.

[Southern Senator North Carolina Yankee]

1956

Exceptionally bad take.  Even if you insist on putting civil rights on a left/right scale as you clearly do, there are a plethora of other issues to consider.

This is clearly the only reasonable way to view the issue. The real question is why you are so insistent on putting 19th century issues of religion/morality on a 21st century spectrum.

Stop trying to make Protestant supremacism seem woke. It's not woke.

1892, 1904, and 1924 are all defensible answers to this question. 1904 is probably the best one. 1952, 1956, 1912, and especially 1948 and 1976 are all terrible answers, with 1912 as probably the best of a bad lot.

I watched a bunch of the videos of Truman given interviews on the Truman Library Youtube channel. In one of the interviews he discusses 1904 though he gets the year wrong, it is pretty obvious who he is talking about. He declines to mention the name specifically "because he has children who are still living". He makes the point that nominating him was a mistake because he was a Wall Street guy himself and thus his attacks on TR fell flat.

However, for what it is worth, Parker attacked TR claiming he was too close to the trusts and pointed to the fact that while TR was railing against them, he took campaign money from them as well and refused to give it back or donate it.

TR also gets a bit of a "more progressive reputation than deserved" in 1904 owing to the fact of how he ran in 1912 in a case of historical back projection. TR was out of step with his party obviously and often drawing the ire of the big wigs within it, but he still had to play nice with a Republican Party that was by this point pushing 40 years bought and paid for by rail and steel in 1904. Furthermore, he often infuriated progressives and socialists by not going far enough. There were calls to nationalize the railways among some Democrats and "very progressive" Republicans, which he rebuffed. Also in the push for reform of the meat packing industry, the whole focus on cleanliness and regulation for the sake of safe food missed the larger point about working conditions and workers rights that Upton Sinclair was actually driving at. He also gave JP Morgan a trust waiver of sorts to allow him to bail out the collapsing firm at the heart of the 1907 panic.

[Southern Senator North Carolina Yankee]

Arguably 1932. FDR heavily bashed Hoover for his reckless spending.

FDR certainly ran as a more traditional Democrat (as it was regarded at the time) but he also campaigned on a "New Deal" however vague that was and later defined that during the course of his Presidency.

Obama also criticized Bush heavily for the deficit. "Borrowing a trillion dollars from the bank of China, raising our national debt" in reference to the Iraq war.

[Southern Senator North Carolina Yankee]

Ford was probably more culturally liberal than Carter, the same might've also been true of Dewey compared to Truman.

In what sense? You seem to be equating cultural liberalism with being more upper class.

This is a pretty major undercurrent in the "party switch" narrative that bears addressing. Especially coming from the likes of Chernow, &c., a lot of it is just blatant classism and paternalistic disdain for poor white people in rural areas of the South and Midwest.

Most of the party flip is narrative is driven by such, a desire to "other" the undesirables and to whitewash history for one's own group to paint them as the good guys.