I just looked up my brochure, I had a VE II Thunder Ute but manual, and the Auto version got the 2.92:1 ratio, while the Manual got the 3.45:1 ratio.
If I were you, If you can afford an OTR and tune, I would start looking around for a used 3.45:1 diff and put that in (don’t do this if you travel long distances on the Hwy all the time), and get the tune done at the same time. There may be a member on here who has a perfectly good used diff laying around with that ratio. A lot of guys upgraded to a 3.7:1 or even 3.9:1 in their manual cars for the extra poke.
If you are not ready to do any mods, look around for a second hand 2.92:1 or take up MrBags on his very generous offer to get you out of trouble until you decide what direction you are going with it. At the very least, you can replace your LSD with the single spinner, and start looking around for a replacement LSD.
Start making calls to diff repair places, you never know what they might have in the shop.
I would also be inclined to take Skylarkings advice after they quoted you for a brand new Holden diff. They didn’t even try and help out their customer by contacting diff specialist. This is probably because they get the Holden diff at a great trade deal, and charge you retail.