After breaking another handle, I found the instructions for installing a posi-temp valve. It did not mention any nuts as suggested in this answer.
I called Moen support at the number listed in the installation instructions. They informed me that the tension on a posi-temp handle cannot be adjusted. From my description of having to re-grip the handle multiple times to fully open the valve, they suggested replacing the posi-temp cartridge (Moen part 1222). They said hard water and some cleaning solutions can build up around the cartridge and make the stem difficult to turn. I installed a new cartridge and handle, which was simple enough, and now the handle turns much easier!
I also found a helpful video on replacing a posit-temp cartridge. This video mentions a special tool to remove the cartridge. I was able to replace my cartridge using only the plastic tool included with the new cartridge.
Kudos to Moen for investing in quality phone support. The first person I was quickly connected to answered all my questions confidently as if they had years of experience with these products instead of reading from a support script.