For all its success typescript demonstrates the downside of this approach. Like you said it's just difficult, and the end result of having every corner of the dynamic language expressible in the type system forces you into the most complex & novel type systems.

IMO a better approach is the one used by rescript and gleam. With a few careful restrictions of the target language you can fit it into a hindley-milner type system. These are extremely well understood, robust & usable, and give you a much smaller interface than the expansive turing complete one of TS.

I'm kind of surprised there's not an active project for a small ML language outputting lua code. I really wish gleam could pick it up as a third backend, it would be an amazing fit.