I just want to send some support your way. I was pretty much in your spot back in May, but desperate to have DS trained before preschool (because preschool requires it). I eventually had to accept that he'd do it when he was good and ready, and not a minute before. I told him so, in so many words, and about a month later he decided he wanted to be trained. We made the deadline with about three weeks to spare.
I don't think newly 3 is all that late for potty training.
(and, FWIW, my son is totally illiterate. )
DC1 -- 2005 DD -- 2009 DS -- 2011