From memory, I would bet that any P4 gearbox would fit the bellhousing, with only the rear mount causing some issues. Maybe a change of clutch plate splines also necessary. My 50 model P4 had a P3 gearbox (with overdrive) fitted and worked fine. Surely a P4 box could be found....depending on your location? Queries are frequently easier to answer knowing the poster's location.
IIRC the P3 rear gearbox mount was a LARGE rubber thing that allowed the box to rotate with engine torque reaction, but not move back or forward - can you check and verify. What has happened to the original box? If you have it, I wonder if the rear case with the freewheel and mount would fit onto a P4 main case....Look up all the australian Rover clubs and see if anyone has a P4 box, and if they know if the P3 rear case would fit. Also early Landy main cases were the same , so see if there are any of the old ones in your area.