I don't follow the premise of the OP?
Does the counter-rotation involve any compressors or just the fan/turbine?
What is the by-pass ratio for this?
If it's a multi-stage large by-pass fan then I might accept an influence on gyro-loads otherwise nil effect.
If talking gyro-loads, where do you expect the weak link to be, is it really the mounts which are easy to add strength vs weight? or is it the blade tip clearances in the engine blading?