I believe I have fixed the problem.
And the solution could not have been simpler. I started thinking that this all started happening a year and a half ago, when our PRV stopped working, and I had a plumber replace it. Today I put a gauge on our hose bib, and saw that the house pressure was 80 psi (Only a little lower than the incoming 90-100). I think he adjusted it so that we'd have a lot of house pressure without it being so high as to cause water hammer. I got thinking about the theory that the fast water/instantaneous low pressure in the starting-up sprinkler line was drawing water from both sides of the tee, so I adjusted the PRV so that the house pressure is 60 psi.
I then tested the sprinklers. No more thumping. I can't believe it was such an easy fix.
Thanks for your help - trying to troubleshoot this one was not fun....