I have a couple of questions:
What year wagon did the 8¼” come out of. I have in this thread
FMJ Differentials (mid-way down) a bit more on measurements (except for axle length), and the change between the '76 to mid-year '80 and mid-year '80 to '89 8¼'s (the older ones are 1 inch narrower than the newer ones are).
Both will interchange with each other – but if you have purchased custom (ie: wide) wheels – then you might have a clearance issue with leaf springs and/or quarter lips if you get the “other” width differential.
The '68 to '96 8¼” use 27 splines.'97 and up 8¼”use 29 splines. There are no 29 spline stock axles that will fit into FMJ's so a person will need custom axles – if you are not able to find a 27 spline limited slip carrier. There were plenty of new and used carriers for these cars a decade ago, but today they are getting harder to find (not produced any longer – I'm guessing).
On an open differential, all a person has to do is change the spider gears to the appropriate spline – for the carrier case is the same between the years. A person “could” do that with either version of limited slip (clutch or cone) – but no one has the spider gears available separately for either version limited slip carrier.
Jeep has an air locking limited slip system as well as an electric actuated limited slip (both in 29 spline) – but either is not worth the effort to change to (both systems (air and electric) were troublesome from the factory).
If you are not able to find a '68-96 limited slip carrier, then getting custom axles made might be the next step. I would remove either axle and use it for measurements.
A few limited slip carriers (27 spline) I found on eBay:
POSI CARRIER DANA SPICER 27 SPLINE TRAC LOC DODGE CHRYSLER 8.25 INCH 10 BOLT | eBay
76-96 Dodge Chrysler 8.25" 3.55 Ring and Pinion 27 Spl Traclok Posi USA Gear Pkg | eBay
Dodge Plymouth Mopar 8.25 8 1/4 Sure Grip Trac Lok Posi 3.55 Gears 27 spline | eBay
Note: I am not afraid to use a used limited slip carrier. If it holds according to factory specifications (ie: you can't rotate a rear tire if vehicle is in park (or in gear) with rear brake(s) off/disengaged and vehicle is in the rear – then I'd use it.
If tire does rotate with car in park and in the air and you can see the other tire spinning the opposite direction, then the limited slip might be rebuilt – depending on which version was installed in car. The clutch type carrier is not too hard to rebuild. The cone type carrier, if not holding in above test, is now a boat anchor or a door stop (for they can't be rebuilt).
Going back to the topic of axles. The rear wheel bearing/axle bearing's inner race rides on the axle shaft itself. When the axles are out and removed, see if the area where the bearing rides at can (or will) catch a fingernail. If so, the axle bearing(s) will need to be replaced with offset bearings (something that is fairly new to the market). The offset bearing uses a different part of axle so axle itself can be reused.
BudW