I just replaced my heater core this weekend. I did it without removing the big black box and without disconnecting my AC, which is full of freon.
I took the dash/dash frame off in one assembly. That way you don't have to deal with the huge mess of wires that are attached to the frame, plus its less work.
First thing, you have to take the glove box out, and the panels under the steering column. Then you can take the whole console assembly out, radio, etc. drop the steering column and lay the steering wheel on the drivers seat. Take the panel off that holds the headlight switch, etc. The switches have locking tabls that you can push in and take the switch out the front to remove the wires. Take the gauge cluster out.
After that, I took off the long screws on top, some are behind the defroster panel, and the other two are behind each speaker panel. Then I took the two bolts at the bottom of the dash off, they hold the dash frame to the body of the car, and they are behind the plastic kick panels right by the door seals, one on each side of the car. The last thing you need to do is loosen the nut on the bracket that holds the dash to the clutch quadrant. You just need to loosen it a few rounds, and the dash will slide off. It takes a 10mm wrench.
I set the whole dash assembly on the floor of the car, with the seats still in the car.
Then I took the hoses off of the heater core.
Next thing I did (I have a working AC and I didnt want to discharge it) was go under the hood and remove the bracket from the AC accumulator (metal cylinder). Remove 2 nuts and the 1 screw in the clamp. It is a little hard, but the bracket will come off and out. Then remove the 2 large nut/washers. These hold the large black box. There are 2 more bolts inside the car above the box, and one below the box by the carpet. It is kind of hard to see.
After these bolts are off, you will be able to move the box a little. Not a whole lot, because remember the AC lines are still attached to the AC evaporator core, which is inside the box.
You should be able to see a little cover on top of the box, and 2 screws holding it closed. This cover is actually held on by 4 screws but if you are like me, and you dont want to discharge your AC, you will have to do it this way, and you won't even see the other 2 screws. The heater core is under this lid.
This is the hardest part... the part that really took me the longest. Try and get the old heater core out without damaging it; its good practice before you attempt to put the new one in. Lift the lid, and prop it open, then pull the heater core out. You really need 4 hands to do this, because it is a pain in the ass. The lid is VERY hard to keep open far enough to get the heater core out. It really helps if you have 1 person under the hood pushing on the heater core pipes. I ended up accidentally cracking the plastic lid on mine on the right corner near the screw hole, which actually made it a hell of a lot easier.
After the heater core is out, the MOST important thing you need to do is scrape all the old glue/sealant that Ford put on from the factory. This stuff kind of holds the heater core in place, but it gets really hard over the years, and it will smash your new heater core when you tighten the lid, causing it to start leaking again within a short time.
After that, I got a heat gun and dried all the engine coolant/antifreeze off of the temperature control door, which has a foam cover on it. In the process, the lid got warm and actually became more plyable. I didn't think about this before, but it actually made it a lot easier to install the new heater core.
After you get the new heater core in, its all back together in reverse order.. of course if you don't have AC, or if yours is already discharged, you can take the whole box out.