I think that's out of scope for the OP's needs/wants. They like TypeScript for catching basic API mistakes, the only thing they don't want is configuration headaches. I didn't get the sense they would be interested in learning a new language for this use-case, especially since I'm going to guess Cloudflare doesn't publish OCaml types for their JavaScript API.
I'm not familiar with opalang, but I haven't noticed size issues with js_of_ocaml (though I've only used it for personal projects). It works by compiling OCaml bytecode to JS. I think the main thing you'd need to be careful about in terms of code size is which libraries you end up relying on.
EDIT: There's also bucklescript, which goes from OCaml to JS (skips the bytecode), but I think it is more relaxed in terms of preserving OCaml behavior. i.e., it relies on how JS behaves for certain operations, instead of trying to preserve how natively compiled OCaml would behave.