There does seem to be discussion at the moment surrounding either replacing Lancaster and Preston hospitals with a combined larger site between the two or simply relocating Lancaster somewhere else and redeveloping the site for housing. If that happens, that may well be solved (and developing that site would arguably be better in terms of reducing car dependence than building Bailrigg). But the hospital is of course just off the A6, so the existing uni bus service would also provide perfectly decent park and ride for that.
Pay more and offer better conditions and you will get staff.
On your first point, I can't see them moving RPH significantly, perhaps they'll build a new big hospital at somewhere like Halton to replace that and Westmorland General.
Bailrigg Garden Village has been approved anyway, so any solution needs to come before any redevelopment of the hospital.
The uni buses would provide perfectly decent park and ride for the hospital from where exactly? Lancaster city centre car parks? Or extend a few to Halton P and R and expand?
On your second point, no way Stagecoach will do this. Because their operating company in the area is Stagecoach in Cumbria and North Lancs, with a huge fleet and driver complement. It'd be a Pandora's box for them to increase for just one opco, then Stagecoach Merseyside and South Lancs will start asking too.
The council could always convince Preston Bus or perhaps Blackpool Transport to try and come up, take over the P and R, build and operate new ones perhaps - but this runs into the similar issues with bus congestion that a service increase from Stagecoach would face, plus issues with locating a new depot etc...
Unfortunately the station stop in post 271 is achieved by reducing the allowances and dwell at Lancaster, which isn't feasible to the extent required.
1 station stop may be possible without major work if it is inserted into the right service, but it is extremely tight on that section for WTT robustness.
Does that change with Windermere electrification, plus potential bi-modes on the Barrow services?