Why not say that `\ @a -> body` infers the type `forall a. ty` where `body :: ty`, and let unification handle the rest?
That's intriguingly simple. I haven't thought through the consequences of this fully, but it does seem plausible. I'm not ready to commit to that, but after a few minutes' focused thought, I can't see any problems with it. In any case, the proposal as written is forward-compatible with such a change, as doing what you say will allow only more programs: ones accepted by the proposal will remain accepted and with the same meanings.
Richard