We're now at five days with no accidents. None.
Some how we finally found the right incentives (bribes) (youtube time and matchbox trucks taped to the wall to help him remember what he wants), and he uses the potty.
Interestingly enough, last week I was almost ready to put him back in diapers, because he just didn't seem to care, and was passively resisting all my efforts. ("Uh-oh! I did peepee on the floor. That is NOT awesome!" he would report.) My efforts were failing, and I wasn't sure that I wanted to fight. I prayed a lot to know if there was a correct answer, and what that might be. While we were failing, he was wearing pull-ups because he's right, peeing on the floor is not awesome (but it is super funny to hear him talk about).
But he was getting a rash. So one day I put him back in underwear. And I remembered, this is what I want. And sometimes its okay to do things according to a parents schedule. That day I was supervigilant about taking him, often, and we found the right bribes, and here we are, with everything working the way it should. It's a miracle. (A miracle that happens for almost all people, but every mom thinks its a miracle every time, I'm sure!)
He's still not good about using the potty outside of the house, but he can hold it for forever, so I'm sure that will come when it's time. I'm so relieved.