The TC is a horrid instrument (IMHO), the design of which makes recovery from any unusual position (UP) difficult as it doesn't respond to g loading the same way as the TS. The gyro in a TC rotates the other way and under reads under loading as opposed to over reading as in the TS. My last flying club had the TCs removed from the PA28s and installed TSs for this reason.
In a previous life as an RAF QFI, we used to teach recovery from the spin on instruments during IF UPs. The standard UP recovery is to remove buffet, then roll the wings level, then pitch to the level attitude - all on the TS as the horizon had either toppled or it's failure had put you in the UP in the first place.
However, if you were in a spin the procedure was chaged. The first priority was to recognise you were in a spin - the definition of which is buffet accompanied by undemanded roll. In IMC, you can definately tell you have buffet, you can probably determine that you have undemanded roll too by your senses. The next step was to stop the yaw by putting the ball in the middle, then remove the buffet, then recover form the UP. Fairly straightforward, worked every time and our students had no problems coping with it.
However, as has been pointed out, the reovery techniques vary from aircraft to aircraft. This teqnique worked for the Chipmunk, Bulldog JP and Tucano (important to close the throttle on the Tuc though) but stopping the yaw and removing the buffet should work on most straight wing aircraft.
Also, I should mention that the CFI of the aforementioned club was BEagle!