I removed the passenger/right side wheelhouse on my 1971 Imperial about a year ago now. My car came from back East but was stored in a barn with a concrete floor so it didn't have too much rust. I did not have to remove the core support but I do recall having to remove a troublesome stud as you are encountering using a stud remover - I let it soak over night using some Kroil as well as all the screws that go around the right front fender opening and it wasn't that hard to do - but get the right tool to do that. There are a number of bolts down in that front leading edge area that seem to take forever to remove and the front of the wheel house is sandwiched between a bunch of pieces of metal up there. One just has to be patient and remove all those vertical bolts up there and it will eventually come out, but for sure it is no fun at all. If you get stuck leave the project for a couple of hours or leave it overnight after getting some rest. Taking some notes or photos of the area during the removal process would likely help in knowing just how the bolts go back together to hold all those sandwiched metal pieces together again.
My takeaway after that job was being grateful that I didn't have to do the left wheelhouse and that some engineer was obsessed with holding all that stuff together and that there should have been a better, more simple design.
In my case, I had to remove that inner fender wheelhouse mainly to be able to access the hoses going into the passenger compartment heater core to replace them since they were the original ones and were held in place with corbin clamps-ugh!! I couldn't really find a better way from underneath the car that was doable mainly because that subframe within the stubframe made that area access really hard. I am not sure what your reason is for removing that wheelhouse but if my issue wasn't yours, you might want to do that job while you have access to that area as well.
