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First, thanks for all the helpful responses.
I am using a high-mass, well-isolated, non-suspended turntable, and the problem is definitely not acoustic feedback.
My tonearm is not damped. There is no well for damping fluid.
I tried the PF-MOD HP-Sub rumble filter from Harrison Labs. At the 20Hz setting there was much less, but still some, woofer pumping which was almost gone at the 25Hz setting. My phono stage has multiple outputs, so I hooked one set of outputs straight to the line stage, and another set with the PF-MOD in-line between the phono stage and the line stage. With my remote, I could A-B listen with and without the PF-MOD. The PF-MOD does filter out subsonic rumble as advertised, but it killed the highs and air - badly. So I took it out of the system.
Next, I stuffed a rag in each of the speaker's woofer ports. This eliminated the woofer pumping, but at the cost of too much loss of bass. So the rags came back out.
Next, I tried a combination of outer ring clamp and spindle weight on the LP. This removed the vast majority of woofer pumping.
I assume now that the primary culprit is record warp. I have a high mass arm that resonates at 6Hz with a test record. Not much I can do about that for now, so my current solution is inner and outer clamps to flatten the record.
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