From my notes, on my 2001 3.0i, I put in about 700 ml of 75w90 GL-5 synthetic gear oil. Of course I filled it to the bottom of the fill plug hole. My 700 ml estimate is based on how much was left in the 1 liter bottle.
It seems fairly ridiculous if it were designed to be filled not up to that point, considering they can put the fill plug anywhere they want. Of course there will be a tolerance, such as at that level or 5 mm lower. Overfilling beyond that level (tilted car, putting the plug in while the excess is draining out, etc.) could cause problems.
I did that when I first got this car, 33k miles ago and nothing has blown up yet. Well at least the differential has not blown up.
Sorry to hear about your problem, and good luck.
And BTW, I think in general the front diffs on these cars tend to be more neglected than the rear diffs. When changing all the fluids on mine after first getting it (not trusting that anything was good), I noticed the rear fluid was not bad, but the front was looking original at 169k miles. Now at about 203k, both diffs and the AT are original and doing very well. I think the reason for the front diff neglect is the need to remove the stiffening plate for access - more easily skipped than the rear diff.