If there was a 269-269 tie and the vote went to the house...

[The Mikado]

I think if there's a 269-269 EV result, you'll have at least one elector go rogue and vote for some random because of the "House can choose between the top three candidates" rule. Maybe a group of electors will force Kasich into consideration and confuse the House vote.

[The Mikado]

If that was the case for 2020 a Democrat would become president and a Republican would become vice president.

Not necessarily. Remember that the next Congress, not this one, will make the decision. GOP could make gains in the House or, less likely, Dems could retake the Senate.

If we did have this particular scenario, with a completely unchanged Congress as laid out in the map the OP made, the GOP wins the House vote 26 delegations to 22, with 2 not voting, so GOP carries the Presidency. Dem gains could push the House to no overall majority, but probably not enough to push the House to a Democratic win.

The tricky thing about the Senate is that it's not clear whether the Vice President can break a tie in a vote on who wins the Vice Presidency, so if the Senate ends up 50-50, we might well end up with a vacant VP slot for months (years?) until the tie breaks.

[The Mikado]

I didn't realize it goes by just number of states instead of EV numbers.

Yeah, it's just number of state delegations. We've only done this nonsense twice, though, in 1800 and 1824, so there's not a lot of useful precedent.

[The Mikado]

Also, a bunch of electors voting for third people doesn't clear up who wins, it just potentially alters who the third option the House can choose from is.

[The Mikado]

I think it's safe to assume, given that the electors are all partisans and usually old hands, that none of them would vote for the opposing nominee. Nevertheless, in the 269-269 scenario, if we don't get that, we might still get the "get a bunch of votes together for potential third option for the House" approach. I don't think Congress is likely to consider a third candidate even if they are hopelessly deadlocked (most of them are from landslide districts for either Trump or the Dem nominee and their constituents would be miffed if they voted for, say, John Kasich rather than either of them), but someone would at least try it.

Not only would they try it, there's pretty good odds it would literally be Kasich. Again, I don't know if anyone in Congress would be inclined to pick Kasich over Trump or the Democrat, but they'd probably get the option.