1999 Ford Explorer Differential Question

Hi, great site here! This question is regarding my dad's vehicle. As an intro, I am a semi-skilled amateur mechanic (I successfully replaced the manual transmission in my 1983 4WD Toyota pickup last weekend, for example), but I have no special tools (like a bearing press or air-powered tools).

Symptoms: 1999 Ford Explorer 4WD 6cyl w/235,000 miles. When the vehicle is accelerating (engine driving the wheels) there is a loud howl coming from the center-rear of of the vehicle. If the vehicle is decelerating there is no sound at all. The pitch of the howl varies with wheel speed (not with engine speed - so changing gears doesn't change the sound). During acceleration from a stop, the sound begins almost right away but at a very low pitch and volume. The sound increases in pitch and volume until about 40 mph, at which point it is quite loud. Then, as the vehicle goes faster and approaches highway speeds, the volume drops off again and is quite bearable - but the pitch continues to increase. There is no associated vibration. Once again, as soon as I let off the accelerator, the sound goes away instantly.

All of this suggests to me that there is some problem with the ring and pinion gears in the differential - probably excessive wear (see milage) or play between the gears.

Of course the thought of replacing the gears has occurred to me, but I also remember from my earlier days that in some differentials there are shims which can be placed behind the pinion gear to reduce play between the gears. However, I have never actually worked on a differential, so I'm not sure how involved this would be.

So, finally to my questions:

1) Is my diagnosis correct?

2) If my diagnosis is correct, is it possible for me to add shims behind the pinion gear to see if that helps before we make the larger investment in a new set of gears?

3) If adding shims is an option, is it a job I can do with hand tools?

4) If I cannot add shims, do you recommend that I replace the ring and pinion gears?

5) If I should replace the ring and pinion gears, is it something I can do with hand tools and "average mechanic" skill? Or is the best thing to just replace the entire rear end?

6) Can you either tell me or point me to a place where I can find out how to properly set the clearance between the gears? I have feeler gauges, but that's it.

Thanks in advance for your help. Of course if you have any questions, please ask right away!