caseywkc - you have ruled out the woofer. Have you tended to the inner passive surround? There's an outer and inner surround.
Here goes a strange and wonderful exploration. I've used my pair of 2.2s as workhorses since 1990 and conducted my early Thiel Renaissance explorations on them. The problem you describe has been considered a design limit since their introduction- although your symptoms may be worse than typical.
'Your' problem actually happens on some other Thiel models, but the 2.2 is the worse. The root cause is electrical field interactions between the woofe, the crossover and/or the hookup wire. Taking the XO out of the cabinet and/or moving it to the cabinet bottom, and/or attaching the hookup wire to the cabinet fixes it. The simplest element of the problem is a feed wire vibrating against the cabinet or driver. But your case sounds more dramatic than a simple wire buzz.
Troubleshooting this problem led me to a systemic improvement applicable to all models, which I call 'Serpentine Feed'. We eliminate potential bucking fields caused by feeding and tapping XO circuits on the same side of the XO panel. By feeding from the back and tapping from the front, fields always blend rather than buck. The improvement is not subtle. I go further in my new XO layout to leave considerably more space around components for more propagation field management. A random element is that reversing feed direction or orienting a coil 180° can fix 'it'.
I don't have a specific 'fix prescription' for your problem, but this is the nature of the riddle. Feel free to contact me privately for further coaching.