SPHLC
Our 'Harry the Staish' used his own funds to send aircrew individuals with long term back/joint problems off for MRI scans. The waiting list to see a specialist was 4-6 months followed by further wait to get MRI. The bottom line is how valuable an asset are you to the sqn/stn? Can they afford to have you off flying?
If you get into that situation of having to wait then Push to Test - go see the Big Man and see if he is willing to cough up the dosh to send you private.
Best of luck