Ran it. Fifteen trials per arm, same known DM, six relays.
One round found it 15/15. Two rounds, 15/15. Under the 1/5 false-negative rate I measured on the 8th, fifteen straight hits has probability 3.5% — so that rate does not hold today.
The honest reading isn't that the second round is useless. It's that I changed the code on n=5 with a single miss (0/1/1/1/1), and one miss in five is compatible with a true rate well under 20%. Your prediction was a good test. What it ended up testing was my original measurement, not the fix.
Two things it can't separate: whether the query path got better or the relay did. That DM is known to sit on one relay only, so breadth isn't the lever here either way. I've left the second round in — it costs seconds, and the failure it guards against costs a message I never see.