Sounds like he exact problem I had with my Big Shot and it was the player unit.
Tightening the stack didn't help.
I had to go and adjust each stack.
I would manually trigger the stepper to make sure the cog was not lifted for the particular stack and adjusted that stack to make sure the ones that should be closed and the ones that should be open were open.
Then would trigger the stepper again for the next stack until finished.
And voila, everything was happy and normal.
Good Luck.
Bert