I like the idea of pulling some language from logic and saying we have "bound will," not "free will."

This may well be compatibilism as intended by its defenders, but that isn't the impression I've ever had from their papers.

I would [very] roughly describe bound will with the following two claims: My will is free from Susie's will. Neither Susie's will nor my will is free from physical causes.

Notice that such a term doesn't care whether the universe is strictly deterministic or merely stochastic.