This is pretty much what I do, except it normally takes about 5-10 minutes of fiddling and swearing to get it right. Maybe I'll get better with practice.
I think this may be the source of my problem. There are 2 long bolts that go through an adapter and 2 thick washers between the caliper and fork, and the bolt head is not flat against the caliper, so the caliper shifts an unpredictable amount when I tighten the bolt. I got the bike (Specialized Crux) used, but I'm 99% sure this is the stock setup (with 160mm rotor).
I'm going to try this. It seems like only the front rotor on one wheel needs to be shimmed to make it work.