I pronounce it CALL-ih-flower, but I know a lot of people from older generations or smaller neighboring towns that say CALL-ee-flower.
It doesn’t surprise me that you don’t do the same “changes” on all words. I say Tues-day, Wenz-day, etc., but I’ve always said caddy-corner.
BTW, I didn’t think it meant truly diagonal, just significantly off from straight. It’s not used often, just for not having your clothes on straight or having not put something in its proper place. For example A picture that is hung off of level is catercorner. One turned so it is diamond shaped is not. A line, on the other hand, is never catercorner.
Very possible, but I picked it up from my Grandpa, so it’s nothing I made up. He’s the one person in our family who still has the old pronunciations, although, as a kid, I thought he was making up words. It doesn’t help that he always said them in a voice that sounded different than the one we were used to.