VMCG .... is the calibrated airspeed during the takeoff run at which, ..., it is possible to maintain control of the airplane using the rudder control alone (without the use of nosewheel steering)
italics added for emphasis.
ATPMBA: nosewheel steering has nothing to do with VMCG as prescribed by FAR25; it may make it possible to control the aircraft in practice at lower speeds, but you may NOT take credit for it. This allows for such events as wet, slick runways or engine failure AT rotation, where the NWS is pretty useless.
The reason you cannot find a definitive statement in the literature regarding VMCA vs VMCG is that one cannot be made; there are too many variables and the manoeuvres are different. It would be like trying to state a fixed relationship between Vs and Vmu. They have similarities, but no hard and fast rule can be applied.
And incidentally, you have more than just rudder in VMCA - you have bank (and hence beta), a pretty powerful influence on VMCA, and also the possibility of roll control limitations.