But yes, the power will be cyclic because of what you just mentioned. However, you may note that the ride is still smooth. You just indirectly mentioned conservation of momentum. Kind of like why does a 4 cylinder car and an 8 cylinder car ride just as smooth? The flywheel keeps a steady pace.

I believe someone mentioned the answer as to just frequently sample. Which is a good approach.

But you did also mention another idea, however, power is greatest when applied at either 3 or 9 depending on viewpoint because going reverse just causes the hub mechanism in the rear wheel to skip. So, regardless of where a measurement is taken, the measurement will be cyclic and an average or integral calculation should be used.

Another idea comes to mind, it is a bit silly. Old fashioned torque wrenches just measured deflection directly by having a bar that is attached to the center where torque is applied, but is left hanging in mid-air. This way when force is applied at the radius the bar does not move from center. Perhaps a high resolution radial encoder could be used in place of a strain gauge if attaching the gauge is a problem.