I managed to fix the wheel. The issue was with the wheel's motor, where the magnetic core had come loose from the shaft itself.
Much thanks to Fikszyn who described this problem in https://www.elektroda.pl/rtvforum/topic3176691.html thread.
The disassembly of the motor was not easy, but manageable with the right tools. I had to use CA solvent to detach the motor's pcb from the housing as it was glued in.
I cleaned the shaft spacers and the magnetic core with solvent and then applied a red loctite and let it cure overnight. After assembly and running the thrustmaster calibration tool the wheel works perfectly!
Here is the video of the core shifting under load https://youtu.be/-fx8ihq2U-g
And some pictures of disassembled and then assembled motor.
Hope this will help all those strangers who wander the internets in search for a fix for TX/T300 wheels with calibration problems!