That’s them telling you they really don’t want the job. A relatively common job is having a truck regeared for big tires, and $1600 would be a little high but in the ballpark for that job. Which would entail a new set of gears, and all new bearings and seals. Throw in another $400 - $1,000 for a new LSD or locker assembly if that’s in the mix. All in, it’s probably an 8 hour job done right.
Most towns of any size have a specialty shop that does 4x4 gearing and lifts. That’s the shop you want if you’re having it internally repaired.
The junkyard stuff can be a bargain, or it can be just as bad as yours or worse. I have used junkyard salvage in some of my builds, but only as a foundation; I take them home and rebuild it before installing