For what its worth heres my twopenny worth on this matter
I had a screaming bevel box but managed to make it very bearable by doing the two following things.
The screaming is a harmonic of the teeth impacts. The imperfections in the teeth surfaces are a factor in the high pitched scream.
1. I had the gears lapped, done out of the box by a specialistengineering company. Backlash setting was recomended.
This makes the wear pattern areas smoother
2. I also then had the gears Superfinished which removed even more high points.
On reassembly, using shims to get correct wear patterns and with backlash set as stated, i found the box much quieter. The screaming was 90% gone.
General noises changed to a different rpm range but all in all i was very pleased.
I am not in anyway engineering minded, and the explanations are just my musings but these things helped make driving more enjoyable.
Good to know, that was the sort of thing that I was thinking of but my knowledge is non existent.