I suspected that when you mentioned your quads as the problem. 2x20's are really designed to develop your aerobic system, and the TSS you get accrue from that shouldn't be so great that you'd be limited to only doing that twice a week (I hate 2x20's so the mental load is huge but in terms of my aerobic system it's not really a problem) . On the other hand, the crank inertial load on a trainer is quite different than what most riders experience on the road and some people are much more sensitive to crank inertial load than others. So when you mentioned muscular stress rather than aerobic stress, that was a clue.

I suspect that if you were to do 2x20's on the road you wouldn't have difficulty recovering.