Err...actually Greg, the fuel burns from inside to out, the inside being a star shape so that the burning surface area stays more or less constant as fuel depletes. The organ pipe gets effectively bigger in diameter as the flight progresses, but the length stays the same.
What is tough is that have lengthened the SRB, relative to the shuttle SRB, by one segment or so, so in addition to lowering the organ-pipe resonant frequency, the longer length de-tuned whatever dead space (I think is was near the nozzle) they had left as a damper. Yes, they can fairly easily re-tune that dead space to damp the longitudinal mode, but it will probably require increasing the length (and thus dead weight) of the motor. Also, knowing whether the fix works or not requires more firing tests, which are expensive and take time. Apparently, the tuned mass damper is an option too - see
FWIW, I worked at Rocketdyne in the early '80's and had the opportunity to discuss the F1 engine's stability with a few of its original designers. The big secret about that engine is it was never really fully stabilized (ok, that's an arguable point, I know, but I'm talking about verbal opinions here, not press-ready official NASA statements) ...it was just made more stable than its initial design (although, describing stability for rocket engines is not exactly a science either). They did also build a few extra 10th's of an inch of copper on the injector faceplate, so that the erosion that occurred there during firing (attributed to a swirling/spinning 1st tangential mode oscillation) wouldn't have a chance to fully burn thru the injector face before the mission duration was up...plus a little extra for margin.