Overfilling adds some drag to the gearbox to quiet things down.

Overfill might not be such a good idea and can cause durability problems while driving due to aerated oil. Aerated oil = reduced lubrication. Another issue is increased fill levels can increase oil temps / decrease life of the oil.

Gear rattle occurs when the gears are worn ( increased backlash ), engine is running rougher than new and / or the center springs in the clutch disc are too stiff. The noise isn't harmful since there isn't any load.

I'd move towards a thicker oil before overfilling, assuming the recommended factory fill level is correct. ( It probably is .) For thicker oil I'd investigate high zinc motor oil ( used on some other brands ) or industrial lubricants where many viscosities are available. Just be sure to use something compatible with brass ( syncro rings , thrust washers ) as extreme pressure lubes ( differential gear lube ) contain sulfur can leach zinc from the brass.

See what Gale Banks has to say about fluid levels in a differential but it will apply to any flooded lube gear system. This is part 1, part 2 has not been posted yet.

Also dig around on the net to see what Gale Banks has to say about diesel smoke and power.

Do Diff Covers Work or Are They Just Bling? Part 1

https://www.youtube.com/watch?v=n4DQ-jzKQRw