The door panels can be removed with door closed – but it is a pain (the newer cars are many more times the pain to open if door is stuck closed).
If you have one working door, try to open door(s) from inside, first. Sometimes pushing on door with handle pulled does the trick most of the time. Changing from front to rear seats can be an issue if you sport a beer belly like myself – but it can be done.
Once open, remove the inner door latches. Once removed clean the hardened grease off with a paint scraper and carburetor cleaner – thoroughly. Once done, use a liberal amount of wheel bearing grease where you can and spray lube where you can’t reach and work the latch my hand a few times and it should be good to go for a few more decades.
The door latch grease used in that time frame gets hard (harder than a rock?) and makes latch operation a pain. I have a similar problem with my ’86 Fifth Ave. The doors open fine but the power door lock aspect of door latches – not so much. The door lock actuator is powerful enough to lock the doors but won’t unlock without trying several times. I need to do the same thing (described above) to it, but what I’ve done sense then is just not lock the car doors (not advisable in some areas).
Once the latches get cleaned and re-greased, they will work like new again.
Until then, be careful about pulling hard on the outer door handles!
Is the rust you have on the front fenders, only?
Looks like a nice find. Other than the woodgrain aspect, I’m almost jealous.
BudW