Thanks a lot, that's really neat! I hadn't encountered the ability to put code directly into the formulas (although I have been using && and || without knowing that was why it works). I've bookmarked the article you shared and will read through it sometime for more ideas.
I did come up with a separate solution that suits my current needs in this situation (and also is Nintex-"safe"), which I'll describe as follows for anyone that wants another solution:
I have the dropdown control and Yes/No control, plus added an additional calculated control. Rather than have the Yes/No control (still named Approval Required) connected to the Approval Required column as it was before, I have the calculated control (named Calc Approval Required) hooked to the AR col. In the calc. control, I put a formula like this:
If(equals([dropdown control name], "[dropdown choice that needs Yes/No as No]"), false, Approval Required)
Here I have false b/c I found from trial and error that Yes/No actually returns true/false.
Then after confirming in Preview that this works, add a hide always rule to the calc. control, and a rule to hide the Yes/No box when the dropdown has the particular value (plus a rule on the Yes/No box to make a selection required when the dropdown doesn't have the particular value).
So while this doesn't directly solve the problem as stated (which is to control the Yes/No box directly), I get a value saved on Approval Required I can use in the workflow, that will be false when the dropdown has the particular value, and the value of the Yes/No box any other time (which is really what I needed functionally).