A couple of issues here:

Swift requires a single header for importing obj-c dependencies. Typically this would be a bridging header that imported all other headers, but clang seems to be rewriting any header inclusions to clang module imports that aren't working correctly when the framework is imported.

I spent some time playing with clang compiler flags to try to prevent this, but without success.

At present this effectively means we need everything in a single header for obj-c.