Installing Axle Housing Seals: How Deep?

To replace the outer seals you have to replace the bearings.... The outer seals are only supposed to retain the grease that should be packed in to the bearing... If the inner seal does it's job & retains the gear oil the grease generally isn't a problem... Make sure to thoroughly clean the bearings & pack them with good quality bearing grease & unless you see leakage I wouldn't replace the outer seals...
Personally I use a grease needle to inject grease in the bearings...

I disagree.

Every issue I have ever had with 8.75 housing's had the same problem, Be it my trucks or cars.

Yes the Bearing should be packed in grease on assembly! If either seal fails you have issues.

If you think replacing the inners are the fix "all" then you may want to rethink things. If the inner is tired then the outer is the same!

You will be back into it in short order with that thinking! Do it once and do it right! JMO!