I recently unmounted, restored and built back together the heater core in my 1971 Newport with A/C. It wasnt that hard at all compared to other work I did on the car (e.g. installing TTI headers lol)
You basiclly have to follow the steps from the FSM, but I will describe it a bit more detailed, or at least try to. While doing this stuff be carefull with the body insulation and the heater core housing, as they contain asbestos. I was wearing a dust respirator all the time, just in case...
1. Remove your glove box door, the latch as well as the upper and lower part of the inner glovebox.
2. Remove the right lower air hose and duct. Remove the left air duct under the steering column. Both are held in place by a single screw to the sheet metal and with a little metal clip to the right air outlet or the outer left duct.
3. Remove the lower foot air outlet in the middle of the car right above the trans tunel. Be careful to remove the 3 screws, which hold litle tabs for cable routing in place. These are hard to reach. If you dont remove these three screw, you will brake the plastic of the air outlet. Guess how I know. The outlet is held in place by 5 screws overal.
4. Remove the center air duct, which directs the air through the cluster outlet. This is a bit difficult with the cluster still in place, but should be doable. It is held in place by a single screw to the lower sheet metal and a clip to the center air outlet.
For info, I had the cluster removed, because I had some stuff to do on it. I guess this made the job a bit easier overal.
5. Remove the air distributer right on top of the heater core housing. It is held in place by 5 screws.
6. Remove the shield protecting the vacuum actuators right next to the gas pedal. These screws were the hardest to reach.
7. Unhook the vaccuum actuator clips.
8. Remove the water hoses going to the heator core in the engine bay.
9. Remove the cables to the fan resistor block and remove the block as well through the glovebox.
10. Remove all screws around the heater core housing by reaching through the glove box and from under the dash.
11. Remove the housing. It may stick a bit. By gentle not to crack the asbestos/plastic housing. It comes out pretty tight under the dash.
12. Remove the heatercore itself. It sticked realy hard to the front housing. Be gentle while removing it. It also comes out tight under the dash.
13. Grab a beer, you made it. Congrats.
I hope, I didnt miss a step.
Installation is everything in reverse order.
As I said, it isnt realy a hard job. Take your time and you will be fine!
I had the core repaired by local shop, cleaned all ducts and put in new gaskets. While I was on it I removed all the stock asbestos insulation and replaced it with new universal stuff.
It is pretty awesome to have a non leaking and properly working heater