An unbalanced wheel will often manifest at higher speeds, but should be consistent at speed, not just when the brakes are applied.
With only the info we have to go on here, I'd agree that the rotors should be looked at. Odds are they are warped.
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Now I just went back and re-read the thread, which makes me want to re-ask Bill'* question (with a word change):
If you don't pump the brakes, instead apply them constantly does it behave the same?
The reason? To eliminate the possibility of an ABS problem.