My '04 XC70 AWD is at 118K mi (150K km). As part of the AWD service, I decided to change the gear oil in
the rear axle diff. (This is NOT about the Haldex -- that was a success).

I pumped out 400 mL of old oil, came out brownish so not too bad. I started pumping in new gear oil

Volvo 31367238 1 L

I was expecting to stop when it spilled out the plug hole, but got to 800 mL added and still nothing. So I stopped there.

I am unhappy with the results. My car is dripping gear oil. The plug was tightened with a new copper washer
(Volvo 11998), and it's not leaking from the plug.

I went back a 2nd time, and pumped out 150 mL, bringing it down to 650 mL. New washer. IT STILL LEAKS.

Where is the leak? Isn't this a sealed chamber?

What is the correct volume of oil?

To clean up the spillage, can I remove the fiberglass "truss" (8 bolts) that sits directly under the rear axle differential? Any hazard to removing this part? Seems like more than just a "cover" having 8 large bolts.

It should be around 500ml. There is a bleeder nipple for excess pressure, which is probably your source of the leak. Remember, the diff oil is a bath, not a submersion.
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Keeping it running is better than buying new

OK. The 2nd question about the fiberglass truss. It looks like it is supporting the weight of the differential gearbox -- is it safe to remove this black truss (8 large bolts)? How much weight is it holding up?

I have no knowledge regarding the 'fiberglass' truss. Any piece of fiberglass, plastic, etc cannot support weight, it will bend. The diff is normally bolted to the subframe.
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Keeping it running is better than buying new