One simple solution is to explicitly state that the limited API does not support subinterpreters.  This is already implied by the fact that the multi-phase init API (PEP 489) requires subinterpreter support but is not part of the limited API.

If we establish this constraint then the problem I originally described here goes away (and we can close this issue).

(Note: I'm pretty sure this is something someone suggested to me at some point, rather than my own idea.)