First of all, I don't know anything about liqui moly gear oil, and I couldn't find very much information on it.
This is copper's original thread on the topic:
901 Tranny gear oil
here's another recent relevant thread:
Redline Oils
copper, did you do the test to see if you have a limited slip differential (from the first thread)?
I would guess that you do not, which makes things pretty easy. The main thing is that if you want to use a synthetic you should use one without "friction modifier", which is the same thing as "limited slip additive". If you can get Red Line 75w-90ns that would work nicely.
However, you did not quote very low temperatures in the other thread, so non-synthetic base oil should be fine. As I mentioned in the second link above, Chevron Texaco Delo 80w-90 GL-5 would work really well, and should be easy to find and inexpensive, but it is very high quality stuff. I think this is the easiest and lowest cost solution, without sacrificing any quality.
If you do in fact have a limited slip, things are a little bit more complicated ... let us know.