Assuming this accounts for the Twins 5-2 head-to-head record against Texas, correct?
There's a few ways things could end up, but the key series and unlikeliest one to play-out is the Texas series against LAA. The Angels, as you said, need to sweep to make this easy. If Texas wins a single game in that series then I think it means Seattle needs a 4-game sweep against Texas, and the Twins will need to sweep both series to close out the season.
Now, as I'm typing all of that, I'm just stoked we're having this type of conversation in the last week of the season discussing post-season seeding in a year that the Yankees will officially be missing the playoffs. Cheers to that!