Drury,
I recently did this swap into the chassis that I'm setting up for my son, and it's nothing to be afraid of. You're going to have some options with brakes. I used the older brakes because your 78 has 11" rear drum brakes vs. the 10" that are used on the 82 axles. This requires changing the backing plate and removing/replacing the rear axle bearings, but it's probably time to replace the bearings anyway. I also drilled and tapped the rear housing top and bottom for zerk fittings to grease the rear bearings. I pull the bottom out and push grease in the top zerk. Instead of forcing grease past the seal into the housing, grease will ooze out from the bottom. While the axle is out, measure and drill between the bearing and the inner seal (can't remember the exact measurement, but it's pretty obvious when you look at it).
Another thing to consider is drilling and tapping the bottom of the hoghead housing (with pipe thread) for a drain plug. This will allow you to change diff lube without pulling the cover and replacing the gasket each time. I also bleed off a little lube when I've been running in water to see what the lube looks like. If it's the very least bit milky, drain it and change the lube. Not worth leaving water in your gear lube.
The front brakes on the 77-78 are large, thicker rotors and the caliper mounts on a ring that bolts over the spindle. I opted to use the older brakes because of the larger size and they are Ford style, where the calipers on the wide track axles are GM style.
One thing that is a problem with the older front calipers is finding banjo bolts. Even 4 Wheel Drive Hardware ONLY offers the newer. smaller diameter banjo bolts.
I will probablyh catch some heat on this, but try switching the gears using the shims from the gears, not the housing (including the pinion shims) and try setting this up in the wide track housing. I have found that about 75% of the time, your ring gear back spacing and pinion depth will be within specs. Seems Dana does a pretty fair job of holding housing tolerances. If this is the case, it's really a piece of cake, if not, oh well... On the AMC, use a new crush collar and pinion nut.
Good Luck. It's not a bad job, just take your time and make sure everything is clean (on the inside!).