But I have similar bandwidth with both the amps and speakers at home, yet don't experience this issue. I am using a Triplanar, which allows for a bit of adjustment of the mechanical resonance by using multiple weights for the counterbalance. My 'table is different too.
Its true that some lathes can impart low frequencies to the LP, but that usually occurs between tracks and also at the end, where the carriage for the cutter head is advanced at a higher rate than during a cut. It sounds like you are getting this pumping during cuts on the LP, so I would rule out the LP as the source.
I would try applying a light grease to the platter bearing, to see if it shuts it up. If so, I would be thinking that the platter bearing is worn as normally a light oil is used.