I'm a bit surprised the valve core can not be removed....but everything is possible.
Second solution:
Remove the hose.
Have the original valve soldered shut.
Cut the original hose and have a new valve soldered on. Any commercial A/C place can do that. Re-install the hose.
refill system.
I'd try a couple of inventive ways of saving that hose.
I know, I'm cheap
This is the type of valve you need,