(I had originally tried replying to my original post about this issue, from a few years ago - I guess Codeweavers automatically locks topics after they reach a certain age? If an admin ever sees this and feels like merging this into that thread, feel free.)
Anyway: I discovered that the 1.1 Patch can be installed so long as the EXE is located inside C:\Program Files\2K Games\Bioshock\Builds.
I had originally been trying with the EXE just at C:\, which hadn't been working, but when I moved it in there and ran it, things appeared to patch properly. So, problem solved!