The problem seems to be room-induced bass modes vs, physical coupling issues.
If you measure and look at the waterfall plot for <200Hz, I bet you will see the sub-40Hz modes pretty clearly.
Bass trapping is one fix you should definitely consider. RealTraps bass traps work wonders on that from personal experience.
It will also require a bit of EQ to remove the final bit. The Audyssey sub DRC box is highly recommend.
And as a final note, physical coupling of subs rarely has much to do with the problem, as a data point, Infinite Baffle subs (like I run) are built into the floor and are part of the structure. Very little energy is transferred to the floor from the 'box', it is air-pressure that causes the floor to vibrate.
Now, some single driver box subs that are too light (and 70lbs is pretty light) can and do vibrate on their feet and generate 'noise' from rattling as they rock back and forth. Isolation pads really do help with that problem. Bolting down the sub to the floor would also address that.