Kasich would sooner set himself on fire than run with Donald.
I don't think so. Of the candidates who did not establish themselves as Trumptard loyalists (i.e. Christie & Carson), you have a handful who have endorsed Trump, to include Huckabee, Gilmore, Paul, Graham, Jindal, Walker, and Perry. I believe that Little Marco has declared himself on-board, as well, pending an official endorsement.
Basically, that leaves Kasich, Cruz, Fiorina, Bush, Pataki, and Santorum as not having endorsed. Douchebag Donald can't really select fellow NYer Pataki, while Cruz, Fiorina, and Bush are all known to loathe him.
I think the most viable options from that list are Walker and Kasich - the two Midwest governors, who have appealed well to their respective states - and Little Marco, who has been viewed off-and-on as a future star in the GOP. I've never really gotten the vibe that Kasich is truly above Douchebag Donald or the vice presidency. Nationally, he is more respected than the other two.