If you have air you cannot service the heater core without pulling the box out and you will also need to pull dash to make it a much easier job.
The dash is not a big thing take the pad off the top and you can see the attaching bolts on each side. There is a brace on the left side of the glove box and there are brackets on each side under the dash. Maybe a dozen fasteners all together. You can get by with just sliding the dash back but you can take dash out and clean everything up.
You need to pressure check the heater core before install I have had two bad ones out of the box in past. I also repaired my air cond. when doing the heater core. My first got the gauges and vacuum pump at Harbor Freight for less than shop wanted to just evac and test the system.
Pull the front seats out first and be very careful getting the drain hose unhooked so as not to break the heater box case.
They sell foam kits to repair foam on the doors inside the heater box.
I also install the wire mesh over the opening coming from the cowl to keep mice out. You can reach up through the cowl hole and add some sealer or POR around to stop the rust and leaks.
Got to the WCCC West Coast Cougar Classics web site and he has video showing how to get the case apart. If you do not do right you will break it. Scrub it out good and if in bad shape you can spray with satin clear to make look new again.
Search the forum some should be lots of info. You can do in a weekend if you have manual to show where the bolts are. There is one hidden under the steering column that you have to drop but not remove.
It is just bolts, screws and nuts not rocket science.
If you have lost the charge in the air there is no problem to unhook. Be careful about twisting the joints and hold both sides with wrenches at the connections.
I also put the mesh wire underneath the cowl vent grills. Check inside your cowl with light and mirror usually lots of nuts stored and might be a nest in there also. You can put Stainless Steel post scrubber pads in the two cowl drains one on each side and nothing will ever get in again.
I have priced doing this job for $500 in the past. I do not have time anymore, lol.
David