We have seen steady and consistent improvement! I have to continually remind myself that it is a process, we are taking the long road, and that he is learning to do something new.
We made it through the whole day without any accidents! I put training pants on him for his nap, and he woke up dry! He went in the potty. He was getting better at it, but still learning to be comfortable with it. He figured out that if he ran, he could hold it longer, so he would run from room to room when he needed to go to the bathroom.
I decided to try to get him to drink more because he can apparently hold it for a long time. He got a lot better at going to the bathroom when he needed it. I stopped giving him rewards just for sitting on the potty–he only got them for being dry and for going. He went to the bathroom more often and with less resistance. He is getting used to it. We went to the library and grocery store, we were gone for a few hours, and he stayed dry the whole time! I was brave and put him in training pants. He did wake up from his nap a little wet, but overall we had a lot of progress, especially in his mental view of going on the potty.