Have you checked your rear wheel bearings? That is also a common failure point on 3rd gen Explorers. Jack the rear wheels off the ground and check for ANY play in the wheel/hub. If there is any at all, the bearing/hub is bad. Don't let that go, as a complete failure will cause the wheel to fall off!
Also, on rebuilding the diff, check before you start the job. I'm pretty sure that the aluminum housing on the IRS rear in these requires special tools, such as a unique spreader tool, to remove and install the carrier from the housing. I believe the housing is "undersized", due to it being aluminum, so you can't properly get it out, or back in, without "spreading" the caps slightly.
Also, a previous poster mentioned something about the bearing "cups" not always fitting, and just not using them. Wrong! If they don't fit, you have the wrong part, or you're doing it wrong, or something is broken/bent,etc... NEVER install new bearings in used races (the proper term for the bearing "cup"). They form a "matched" wear pattern over time and should replaced as set.
If you have never done this before, I wouldn't try your first rebuild on this rear, as it seems to be particularly sensitive to precise correct setup of the clearances. Either buy a complete unit, or have it professionally re-built, by a shop with experience with this particular rear. Ask them about setting the clearances, backlash, tooth pattern,etc... If they don't know what you are asking, or say that they don't bother doing all that,etc... then find another shop.
