I'd say fuck it.
Its an impressive "party trick", but given your history of shoulder problems and desire to get strong, spending 3 months trying to do a high rep set of overhead squats seems like a waste of time IMO.
If you want to get good squat form, practice squats.
If you want to get flexible, stretch and do mobility work.
If you want to strengthen your back, start light with squat and deadlifts and work up. You can make it a long way in 12 weeks, especially if your not beat up from rugby.
Making it your sole training goal is just plain stupid and belongs on a different message board. If you want to practice the lift, do it, but 80% of the progress you are going to make will be from doing squats and deads.