I'm pretty sure what you're getting on the stiffer shafts is a false weak, where the shaft is bouncing off the strike plate so that the nock end is coming off the rest to the left. If you're getting good bare shaft flight out of some combination, probably the .600 spine shaft, then that's where you want to be. You might be having some fletch or quill interference with the fletched arrow, which you can correct by rotating the nock until the fletch interference goes away.
How is your form? That can cause problems with tuning too.