Why the woofer moves badly when playing certain LPs

Actually, many of the lathes now being used have been rebuilt (having been recently rescued from years of storage) to better-than-new condition. Your problem may be that modern mastering avoids the use of the bass filtering that used to be common practice: rolling off the very low frequencies contained in a recording so as to make groove tracking by cheap, mass-market cartridges less demanding. Some current phono amps (Herron for one, I believe) include a rumble filter.

@mijostyn  I highly doubt that mastering lathes are to blame- too much is at stake! I have yet to buy a new LP and run into anything like this; OTOH many of the new LPs I've bought seem to have deeper bass than many of the older LPs (I like electronic music...). I did run into one LP which was overcut, causing distortion on bass notes, but overcutting is simply a mastering error on the part of the mastering engineer. 

One fairly simple explanation for the complaint is the cartridge has compliance too high for the mass of the tonearm.

Have you looked at the records to ensure they don't have any warping, or that they are sitting flat?

You are getting the woofers pumping due to feedback.  The stylus is picking up the airborne sound and re-amplifying it.  Either relocate your turntable, try different platforms and if all else fails, buy a KAB Rumble Filter for $179.00 from KAB. That is what I had to do and now I am a very happy camper.