Though it was never officially dubbed "Stage III", I thought it apropriate to do so to go along with the Mustang and Truck Roush Stage III vehicles. Stage I vehicles received an appearance package (body panels, paint, graphics, badges, etc). Stage II received a suspension package (components listed in the Stage I and II page on this website) and Stage III was the drive train upgrade (engine, transmission, rear). So again, the GTC with the JRPE drive train upgrades is referred to as a Stage III car.
GTC cars sold with the Stage III package went to Jack Roush Performance Engineering (JRPE) in Michigan, USA and had their 5.0 H.O. engines replaced with a 5.8 H.O. engine built by JRPE. Paperwork from one of the owners of a GTC indicate the numbers for the 351ci engines were at 300hp and 350lbft of torque. Back in 1985 this was twice what came in the Mustang GT 5.0 H.O. engines.
Customers were given the choice of either keeping the AOD (4 speed automatic) transmission or an optional 5 speed manual transmission with leather wrapped Hurst shifter. These are super rare in that only three (3) GTC cars are known to exist with both the 5.8 H.O. engine along with the 5 speed manual transmission. And of those three, only two (2) have all three stages ordered...I, II, and III.
In 1985 the factory default rear differencial in a Mark VII was a 3.27:1. Customers could order one with a Traction-Lok differential instead of the conventional rear. The Stage III cars had the 3.27:1 gears replaced with a 3.45:1 Traction-Lok.