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probably around 100-200 depending on who's doing it. I had a electric locker installed in the front but was thinking it was around 200 for the work. Its been a while though so not totally sure.
I would expect to pay around 3 hours worth of labor. That seems reasonable to me. Gear swaps are more expensive because you have to deal with setting up the pinion too.
The time it takes somewhat depends on the adjustments that may need to be made. Get lucky, the new one drops in place of the old one. Have to make several adjustments to fine tune could take longer.
Keep in mine $$$$ depends a lot on the area and labor rate and who is doing it, which is why I gave it to you in hours.
I do something in my garage at home it's much cheaper than a shop doing it.
Make sure they check the tooth contact pattern, even after just swapping the differential itself. Once you get into aftermarket carriers, and even with the stock OEM stuff, it's always a good idea to check contact patterns.
I priced having Detroit Truetracs installed in both ends of my truck. I went with a shop that does axles as its main business so I'm sure they are proficient with all aspects of it. It was about $2600 for everything, and that included the Truetrac units(around $650 each), axle rebuild kits with new bearings and seals($250 or so each), checking and adjusting the tooth contact pattern as needed and labor. I'm in CT so labor rates are probably a little higher here than other areas due to the general cost of living. This price was within the last year. I would like to get it done but something always seems to come up that has a higher priority in the budget.....
I would not do a full locker like a Detroit unless your mostly off road. The vehicle looses alot of its road manners and can be dangerous on slippery roads at speed. Unless your mostly off road i would consider a Eaton electric locker, True Trac, or Eaton limited slip. All these units will work much better than even a new factory limited slip. Both the True Trac and E locker can be used for front end applications. The advantages of a limited slip is that its automatic where the electric locker will need user input. However the locker could do a little better in some situations like rock climbing and when the truck is leaning hard to one side or the other. In just mud all three systems work very well.