Green threads done right strikes me as something like Windows' user mode scheduling (or Google's switchto patch that sadly never made it upstream), in which threads really are 1:1 as far as the kernel is concerned, but manually scheduled by userspace. This requires kernel support, but it fixes every issue except preemption, which is better to just not fix. (Few Go programs actually benefit from multicore CPU scaling; for CPU bound tasks a better use of optimization time is just not writing in Go, which tends to result in better speedups than trying to scale Go due to Go's compiler being relatively immature.)
In my ideal world, kernel-scheduled and user-scheduled threads would exist in the same language, and programmers could choose which one they want on a thread-by-thread basis. I/O calls would be equally compatible with either threading model (which could be done in a zero-overhead fashion with the proper kernel support), eliminating the problem of sync/async incompatibility. This can only really be done today on Windows, unfortunately...
If you're doing a green threads implementation for a high level language runtime, those restrictions don't apply, to an extent. I think e.g. Erlang, Haskell or Go are examples of "green threads done right".
(Now, I do think Rust did the right thing in getting rid of green threads, but that IMHO is more a result of the space Rust is in rather than a general indictment on the utility of green threads)