I think that Whig-Republican-Democrat (in 1868 and 1872)-Republican was a pretty unusual voting pattern. It kinda sounds likes a
Liberal Republican, but the defection in 1868 doesn't fit that pattern. 1876 is also really problematic here. I could see someone who generally liked the Republican Party but was strongly anti-Reconstruction defecting from the party for the three elections from 1868 to 1876, but it's hard to see someone like that deciding to return to the party in 1876. It's also pretty weird to vote Republican in 1856 but Democratic in 1868, and the 1856 vote rules out a lot of people in the border states.
This sounds like a Whig-turned-Republican who holds a very strong personal grudge against Grant. I guess it's possible that this is a former Whig who hated Reconstruction but figured it was basically over by 1876 regardless of the results of the election.
Also, this is off-topic, but I've always found it interesting that, in the aftermath of a major war and going up against a war hero, Seymour was able to keep the 1868 election fairly close in the popular vote.