Actually, not to worry. I sorted it out with a second mask underneath it, and can work with its opacity and feather as much as I want. Works perfectly.
> For example, imagine a pizza, with one slice visible and the other seven being 20% visible.
Have two masks on your layer. Have one mask the shape of a single slice, and the other mask encompassing the rest of the pizza. Set opacity for each individually.
> The mask opacity only changes the opacity of the visible pixels, which seems rather ridiculous given that I can change that with its own opacity controls.
It's not ridiculous, for the reason demonstrated with the solution that I provided: you can have multiple masks, each with individual settings for the opacity of the non-transparent pixels that they define.
It looks like you posted again while I was typing my response. Glad you got it worked out.