Good Morning Garance & Rosalie
I also have the frozen neck/shoulder problem and for a while I would not drive because of the parking difficulties. My answer to this was to fit a rear proximity detection device, one of those contraptions which bleeps when there is something close behind, mine has an indicator which shows the distance to the nearest object behind.
To reverse park I lower the door mirrors so that I can see the white lines ,or pavement edge, and use only the mirrors I make no attempt to turn my head.
With the aid of this gadget I changed from being a lifelong failure at reverse parking to an expert in the space of a couple of weeks, I can put the car central between the white lines of a parking bay and six inches from the nearest object behind ( even if it is only a cat refusing to surrender territory--as cats do)
The gadget cost£40 but i don't know what the fitting cost would be (i installed mine myself)
If you are in any doubt about using only the mirrors watch a driver park an artic.he won't turn round.
let me know if you want any details about the device.