You may have a cartridge tonearm mismatch. This will cause the kind of large subsonics you are reporting. You can try either a subsonic filter or a different cartridge.
Also check that the cartridge is aligned properly. Get a stylus protractor if you don't have one. http://www.vinylengine.com/
They have a large selection of downloadable protractors.

I'm afraid a new cartridge won't help much. You are simply seeing the subsonic output from a poorly designed tonearm. Going to a less compliant cartridge might result in less woofer motion, but it is unlikely to eliminate the problem. If there is no subsonic filter you can engage on your pre amp, you should be looking for such an item as an outboard add on. Give these folks a call, http://www.hlabs.com/technical/crossovers/, I think they can set you up with a plug in filter for a few dollars. Or better yet, just dump the Technics on some unsuspecting teenager and buy the better table and arm. You won't know what's actually on your vinyl with the vintage Japanese table.

I wouldn't give up on the turntable just yet. You could have a cartridge/arm incompatability issue, but it could also be several other things. Many times, the woofer pumping will gradually decrease as you get deeper into the tracks of the record. Warped records, even very slight warps will cause woofer pumping, particularly toward the outer tracks where the warp will be most prominant.

I would at least try a couple of observations as to whether the pumping action changes between different albums, different points on the album and with and without the mat in place. Some cartridges clearly don't mate well with some arms and a simple cartridge change and/or record clamp could cure or vastly improve the problem. Heck, your cartridge could simply be a bit out of line.

This is not an uncommon problem and one that should be relatively easy to either improve or correct.

Vibration isolation is not likely contributing much to the problem. More likely, the cartridge and the arm just aren't happy together. Grado cartridges, for example, can be very finicky with Rega arms.

The most likely issue is one of having a cartridge that is high compliance. A stiffer (lower compliance) cartridge would probably mate better with the arm. The pumping action is caused from very low frequencies from the cartridge being transmitted to the amplifier, which actually makes the amp work harder and robs the system from dynamics. We're talking below 12HZ frequencies that are being amplified. Since we can't hear frequencies that low, but speakers react never-the-less, the speaker is acting like a super-duper subwoofer with no sound. The most out of control pumping comes from around 6HZ and at louder levels you can certainly expect the motion to be at its most lively.

It used to be that preamps would have low filters that you could engage and get rid of the pumping. I mentioned making the observations to see if perhaps you had a bad mat that was creating the warp in all your records. Taking it off would answer that question. If it still pumps wildly, I would probably try a different cartridge as the most likely solution...or the filter suggested in the previous post.