Daniel, thanks for checking this out so quickly. My old remote is an RM-VL900 and you're right: something went horribly wrong between these two models.

Anyway, I just tried again and the problem is at step 5. When I press the target button and let go, the SET LED flashes quickly (much faster than the usual 3-blink OK) and then it and all the lights turn off.

I guess I got a lemon. I talked to Sony's tech support and they gave me an RMA, but I'm thinking I might be better off just returning it and trying to find a 610.

Thanks again for your help. I wonder how widespread this problem is.