T.S.
Oh please don't give them the option of using in a pullup, that just creates a power play, something you DON'T want to deal with, especially if they are training so well!
My son was only 22 months old when I trained him, and while the big potty was okay at home, public ones scared him (Hell, don't they scare all of us? lol!)
Since public toilets don't usually have stools I just got into the habit of holding him up over the potty in my arms and helping him aim. I tried to make it silly and fun, and I never did the flush (loud scary part) until we were done with hands washed and he could put his hands over his ears. That seemed to help, and again added to the "game" aspect of the whole thing.