Vmca and Vmcg
An important factor to bear in mind is that for most aircraft Vmca is essentially determined by a static force balance and can be relatively easily approximated analytically. Whereas Vmcg is by its nature a dynamic manoeuvre and is not at all amenable to analysis. Therefore one cannot make a firm statement about the relationship between Vmca and Vmcg.
If one just considers the static force balance in the yawing plane, then care must be taken to include all the sources of yawing moment. In particular, when considering moments about different points (such as wheel and c.g.) all the relevant differences should be accounted for.
For the Vmca case, the moments concerned are, as noted, the engine-generated yawing moment and the rudder generated restoring moment. Considering only these factors, Vmca would be the lowest speed at which these two are equal.
For Vmcg, if one considers moments about the main gear (using the inboard wheel) it does appear that the engine moment is increased and the rudder moment decreased, as you suggest. But if one continues to consider the c.g. as the point of reference then the moments are seen to be equally balanced. As a body is in equilibrium about all references points at once, it is clear that there is an error in the logic.
The problem is that in choosing to take moments about a wheel, account must be taken of other factors. In particular, the acceleration of the aircraft down the runway generates a considerable inertial moment.
The actual reasons why Vmcg is often lower than Vmca are far more complex than these. Factors which come into play are:
1. Vmcg is a dynamic manoeuvre where the restoring force is applied after the disturbance, and must be capable of more than balancing[ the engine moment. This generally will require a larger rudder moment than for Vmca and so a higher speed.
2. Vmcg is conducted at or near zero angle of attack; Vmca is conducted at low speeds and high angles of attack - often at or near shaker/stall warning. For many aircraft rudder power is a powerful function of angle of attack, and the reduced rudder effectiveness for Vmca requires a higher speed to generate the same moment.
3. Vmca is defined as a static trimmed speed (ignoring the other Vmca requirements for simplicity). Vmcg is the speed at which the engine is assumed to fail; by the time the pilot has applied full rudder the speed may have increased several knots, and so the speed at which the moment balance occurs is slightly higher than the declared Vmcg. This tends to relatively lower the value of Vmcg.
4. Vmca may well be limited by factors other than rudder power; the aircraft must be trimmed in all axes and so other controls may actually be limiting. They may also be producing significant yawing moments themselves, further complicating the balance. These tend to increase Vmca.
5. Vmca is helped by a high directional stiffness (Cn-beta or Nv) and a low sideforce coefficient (Cy-beta or Yv) as these combine to allow a high beta for a given bank limit and a high restoring force due to beta. Vmcg is broadly neutral for these parameters - high stiuffness reduces the initial deviation but makes correction more difficult. Low sideforce again reduces the deviation and reduces the correction. For Vmcg these aerodynamic factors can be lost in the landing gear effects.
If one combines all these factors then often item 2 is an important reason for Vmca being a higher number. But it is by no means required to be that way.
(Incidentally, my current aircraft has Vmca higher than Vmcg)