I've used Mobil 1 75W90 in both Roadsters, based on advice from "the two Johns" that posted here for years until they sold their cars.

 

Then don't worry so much about the specific product, think more about changing it every 75,000 miles or five years, whichever comes first.
I am **** about 229.3 approved engine oils, but Im not all the concerned about the differential - it's a differential. 75w/85 maybe up north, 75W/90 here in the south.

 

Paranoia perhaps, but I sensed that the rear end was starting to whine just a bit. So at 60K miles I settled on the Redline 75W85 differential oil. Getting oil into the differential is another matter. Followed the advice to make sure the fill plug was loose. (14mm male hex head socket). I drilled a hole in the cap of the Redline bottle to accept a 1/4 pipe nipple attached to a piece of clear tubing. I was able to shove the bottle up in the suspension and hold it there with a bungie cord while it drained into the rear end. Since the oil is rather viscous, I punched a small hole in the bottle at its highest point allowing it to flow better. It would have been a lot handier to have some sort of pump or squeeze bottle. I will re-check the level next time the car is up in the air. Can't road test right now because of the road salt this time of year in my area.

 

Anyone know HOW MUCH DIFFERENTIAL LUBE TO PUT IN?

I have the Chrysler Crossfire manual, and it says to service it per "Maint Manual 3-40 Rear Differential Drain and Re-Service" which tells you to drain it completely, and then tells you to "Fill the real axle (This is NOT A REAR AXLE, It is the DIFFERENTIAL, which is a COMPLETELY different animal, and is just PART of the rear axle!) to proper specifications".
It DOES NOT SAY what these magical specifications are, or where they can be found. I can tell you that THEY ARE NOT ANYWHERE IN THE DIFFERENTIAL OR REAR AXLE ASSEMBLY MAINTENANCE MANUAL INSTRUCTIONS, AS i HAVE BEEN THROUGH THEM PAGE BY PAGE.
Anyone have an idea of the amount of differential lubricant to install in the differential?
Thanks very much!

 

You are making this way harder than it is.
I bought two quarts and had a little left. You fill until it starts to run out of the fill opening.

 

Thank you very much!

 

Here's a post I did when I replaced my gear oil. I hope that it is helpful.
Like pizzaguy said, fill it until it drips out. IMPORTANT: Make sure to remove the fill plug first, drain plug second.

LINK to rear gear oil replacement.