Hmmm... it still seems to me that you might have different theories of (say) the electromagnetic wavefunction. These are different mathematical structures that you hypothesize it might have. The theory claims that the physical object is in some important sense isomorphic to the mathematical object, and thus you call the mathematical object the theory. But the theory is still distinct from the wave itself, at least as I see it.

This does get close to some important questions about the way mathematical modeling works though.