As far as I know, those are not obsolete. There is nothing obvious in the HTML 5.2 standard docs that would indicate they are.

4.01 Transitional was supposed to be a temporary crutch to bridge the gap between the "anything goes" era of HTML 2/3 and the formal 4.01 Strict spec. So, yes, the verifiers will indeed accept pretty much anything. It just wasn't supposed to survive ~15 years ;-)

(And I'll join Crazy: if you need a hand converting or testing, please let me know.)