The following is based on the assumption all electrical connections have been checked, the output sensitivity of the new cartridge is matched to the phono preamp to assure there is no overload/clipping, the preamp/cartridge Capacitance has been matched, and the only change is new cartridge. Then, potential root causes of woofer pulsation when playing vinyl records are, without limitation: 1 Warped Records, 2 Turntable Rumble, 3 Turntable Isolation (proximity from speakers, suspension adjustment, racking/platform), 4 Speaker to Stylus Feedback Loops, and 5 Tonearm Mass/Cartridge Compliiance Mismatch. From what you have stated 1 to 3 can be ruled out, and you correctly identified 5 as a possible root cause. Reinstall the original cartridge to see if this resolves the issue. Check compliance recommendations for your tone are and stack the recommendations against the cartridge specification. This should give you information to determine if 5 is the root cause.
If the new cartridge is higher compliance compared to your older cartridge, then I would also experiment with 4 by repositioning the TT further from the speakers. While 3 is a remote probability, you may want to experiment with your TT suspension to see if that resolves the issue
Distortion on only the outer record groves and not the inner groves is normally an alignment issue or an anti-skating issue. Double check both to the cartridge manual specifications.
Rumble filters are an option, but, IMHO, I would avoid them.
Good luck,
John