I have a 91 Explorer (2WD) with just over 200K miles on it
and as you would expect, it has some wear. My question
is if anyone knows if it is possible to adjust the rear end
to remove excessive play in the gears. Sometimes when
transmission upshifts just as I let off the gas, I get a loud
clunk in the rear end. Other than the clunk, everything
else seems to work fine and there is no howling or grinding
noises, or vibrations.

Haynes manual says repairs are beyond the scope of the book, so
I am left hanging. Axle code is "43"

Just wondering:
Dialtone

 

You would have to buy the explorer shop manual from Ford. Setting backlash and pinion gear endplay is very tricky and the gears will sing if its not just right. You'll need access to a press to press the bearing off the pinion gear to remove the old shim as well. Its very tricky stuff, if its not too big of a problem i would leave it alone.

Justin

 

Have your U-Joints checked. They could be worn out. Listen to hear if there is a high pitched squek when you accelerate. It should increase as the vehicle speed increases, then go away. If you are mechanically inclined, get under the vehicle and try rotating the driveshaft. If there is play in the shaft, I would guess your U-Jints are shot.
Also, while you are under there, try tightening your pinion nut. Sometimes they can back off and leave play. Left alone for enough time, you will run into a grenaded rear end.

 

With 200k miles, you may want to pull the cover off and
take a look inside. Check the small gears in the center and
especially the shaft for play in the housing.

 

You are experiencing the same symptoms of my 86 Bronco. We pulled the cover off and found all of the slop (free play) in the small spider gears. The ring and pinion were actually in pretty good shape. I took this opportunity to install a Ford Traction-Lok differential and it cost about $350 back in 1992.

I recommend that you have a axle/drive-line shop take a look at it. I think they are a little better equipped to deal with this problem rather than some of the dealer nowadays.

FordFool