Got a reply from John at LM USA. He confirms the approximate flow rate should be 500 ml per minute, +/- 10%. He did a test on a new GS/3 and it ran 400 ml in 50 seconds before the cutoff. Ken's flow rate is within spec, mine isn't.
John is guessing that water destined for the brew group is partially being bypassed backwards through the check valve, B.2.008, between the hot water mix block B.2.007 and tube T.2.105 (page 6 of the part manual, for those of a technical persuasion.) Below is a picture of the part in question, labeled "J".

John thinks something may be blocking the check valve open or the part has prematurely failed. I've asked John how to proceed. I'm guessing drain both boilers, remove the check valve, clean/clear it, and see if that fixes the problem. If not, replace the check valve. I've also asked for tips on getting the check valve out. Judging from the picture, it doesn't look too hard, but you never know.
On backflushing, I've also thought that with the automatic cycle you don't get the benefit of the detergent sitting in the machine for a few minutes. I like Ken's suggestion to do a manual detergent backflush for that purpose, followed by the automatic cycle (plus another cycle with clean blind PF to clear out the detergent.)
BTW, based on a post on Gs3cafe, I've been conservative with the amount of detergent: only 1/2 tsp instead of the full tablespoon recommended in the manual, which seemed like an awful lot to me. Any suggestions on that, Ken?
In any case, whether or not there's gunk in the check valve or anywhere else in the water path, I'm not going to do any more backflushes, plain or chemical, with a dirty shower screen in place! This will probably lead to cleaning both sides of the shower screen more than once a week. Seems like a good idea to backflush with a clean shower screen in place, rather than without the shower screen as instructed in the manual, to avoid any possibility of solid particles getting into the water path.
On pressure being different at the group head, that doesn't surprise me. As I said, my method of adjusting the flow rate on my home-made PF gauge probably isn't accurate enough. The gauge is more useful for measuring blind pressure, and there it agrees with the built-in gauge.
I guess the real issue all along has been flow rate, not pressure. This probably explains why the shots haven't been adversely affected, just the timing.