And all probable causes...  you ran the bearings dry, and they've worn
grooves into the races.  Depending on how much heat was generated, the gears
could have suffered damage as well.

If you're a competent DIY-er, have access to or can rent the following
tools:

bearing splitter
shop press (not exactly required - but would make things a little easier)
dial indicator and adjustable base
inch-pound torque wrench (beam or dial - click-type won't work)
foot-pount torque wrench
slide hammer with 2 or 3-jaw puller attachment
Chrysler differential adjuster tool (can be made from simple components if
you have a welder or someone who can)

You'll be replacing all bearings (carrier, pinion, and axle), and possibly
ring/pinion gears as well, depending on how they look.  If you can do it
yourself, you'll be looking at about $300 in materials (or a little over
$100 if the R&P are still salvagable), and probably close to a day's worth
of work.  If this is the route you decide to take, we can talk about
specific steps and procedures.

A shop would probably charge you around $400-$500 in materials, and 4-6
hours labor.  You can calculate that based on the going shop rates in your
area.

If you can find a used axle with the correct gear ratio (only really
critical if you have 4WD - otherwise, any gear ratio available in those
axles that's acceptable to you will work) for a good price, it would save
you a LOT of time (essentially, unbolt the old one, bolt in the new one, and
bleed the brakes).