Does OP know any carrier that officially allows folks to swap between cabins halfway through a flight or so?

I don't and while certainly one can ask (way better than just blatantly doing it as some would), the swap should be done before the flight or right after take off (when safe) after informing the crew.

Everyone getting a few hours of decent shut eye in a J seat (or F seat) while the other person is in Y is certainly a nice prospect, but more like a crew rest rotation and airlines are not in the shareds seat business.

I have seen some swaps allowed for landing, e.g. a less mobile family member could be in J seat and more nimble, younger person in Y (who was originally in J) as they needed to catch a connection or so, but not the norm and certainly not swapping mid-flight.

Some folks also try to smuggle smaller kids from Y into J (not lap children) for sleeping or so as SQ seat is quite wide and could accommodate slim adult and kid (though I don't think comfortably), but if discovered the crew should / would ask this to be stopped and each to return to their booked seat. YMMV.