Sorry for the late response to this... been at sea.
In my opinion, synthetic fluids will hold up significantly better than petroleum based fluids in the high temp conditions of a tranny (or diff). However, using the correct fluid which meets the manufacturers requirements is still necessary.
I'm not positive, but believe the GTO requires a transmission fluid meeting GM Dexron III requirements. Many synthetics, including Mobil 1 Synthetic ATF meet this standard and are appropriate for use in the GTO. Mobil 1 also makes a synthetic diff fluid that meets the requirements for the GTO, the Mobil 1 Synthetic Gear Lube LS 75w140. Mobil 1 states this fluid has limited slip additives in it, and does not normally need the limited slip additive from GM. Like AMSOIL, Mobil 1 also states that in some applications, OEM specific additives can be added.
As an alternative to Mobil 1, I know these fluids do meet Pontiac requirements for the automatic GTO:
AMSOIL ATF
AMSOIL Severe Gear Extreme Pressure Synthetic 75w140
As a note, this gear lube also has the friction modifier already in it.
Diff takes two quarts, auto tranny takes 11 quarts total fill and around 5.3 quarts for a drain and fill. :cheers