Ah, this behaves oddly if you give the module a name of an existing module in the package set. For example, if I call the current module Data.Semiring and try to use + within it, then I get a "ReferenceError: $foreign is not defined". Perhaps I should rewrite the module name to Main to ensure that it doesn't clash with any module name in the package set?

This now seems to work even if I try to redefine an existing module. I haven't been able to think of a way that rewriting the module name like this would be an issue, it seems like a slightly nicer UX for what is essentially the same idea (only modules with a specific module name are allowed).