how can VMCG be greater than V1 on transport category aircraft?

Answer 1

Dennis, I am sure you meant to say MINIMUM Ground control speed, not maximum. VMCG is exactly what you said it is, but it is a minimum speed not maximum. Check your AFM 51-9, I have a digital copy if you would like.

Answer 2

VMCG, Minimum Ground Control Speed, decreases with wet or icy runways and the amount and degree of crosswind.
It is also based on worst case scenario of loosing an outboard engine, using 50% Aileron deflection, full Rudder input and nose wheel steering. Being able to control aircraft on the ground.
V1 is GO speed, point of no return which you are commited to takeoff.
If V1 is less than VROT, Rotation Speed, you have a split marker condition. Under this condition you will still be on the runway and commited to take off from V1 until acceleration to VROT.
If VMCG is less than V1 you would not be able to control aircraft in case of engine failure before VROT, resulting in an unsafe condition. Takeoff will not be attempted.
If different runway is available with less crosswind or reducing gross weight of aircraft can increase VMCG.
Reducing Gross weight will also decrease VROT until it is equal or less than V1. Then VMCG is no longer a factor.