(Mid)west coast drive?

[Alan Anderson]

Unpowered wheels rob you of potential traction. You want every weight-bearing wheel to contribute to motive power.

[Joel Glidden]

Your maximum pushing force is equal to,

Mu * M * g

Where Mu is the friction coefficient of your wheel material on FRC carpet, M is the mass of your robot carried on driven wheels, and g is gravity. This assumes your 3 CIM gear boxes produce enough torque to slip the wheels. If that is not true, then your max pushing force will be lower. In either case, the number of wheels touching the carpet is irrelevant unless that number is less than 2 in which case you may have other problems.

Your mentor's suggestion has the potential to reduce your maximum pushing force, but it might be the lesser of two evils if your cantilevered shafts aren't up to the task.