I got brave and let him take a bite. Or two. Or three. Or ten.
It didn't break the skin or hurt at all. Either he went easy on me or that's the best he can do.
I tried to coax him onto my open hand later, using a few different seeds as bait. He seemed puzzled and bit me a few times. Again, no pain or blood shed, but he was pretty determined to make my hand go away.
I think his biggest problem is that he closes his eyes when he puts his face near my hand. He goes into cautious, defensive mode. I guess he's protecting himself in case I attack? His vision is already bad because he's a mouse, but with his eyes closed he can't see where the seeds are to grab one so he just bites at random with hope that he'll find an edible snack.
Anyway, I think this was a huge step in building trust with him. I wish someone had told me that the bites didn't hurt or draw blood. Is this really normal for a domestic mouse?
When he climbs up at the door, he's starting to look down at the table more often as if he's tempted to jump down. I still try to avoid giving him any treats when he's there, and instead give them to him inside his cage.