When we have two wheels spinning in opposite directions the torque is
tau = I*domega/dt + I*d(-omega)/dt = 0
The gyroscopic effect doesn't actually make it harder to turn a wheel. It's just that if you turn it in the xy-plane, it automatically turns in the direction perpendicular to the push (the yz-plane). When a human is physically turning a wheel he will try to stop that from happening, thus the feeling that it's hard to turn the wheel. Note that in particular the gyroscopic effect does not produce any force in the direction opposite to the pushing force.
You have a wheel spinning one way, and say that if you try to turn it clockwise in the xy-plane then it will turn clockwise in the yz-plane because of the gyroscopic effect. If you have a wheel spinning the opposite way, and if you turn it clockwise in the xy-plane then it will turn counterclockwise in the yz-plane because of the gyroscopic effect. Adding the two effects cancels them.
You have a wheel spinning one way, and say that if you try to turn it clockwise in the xy-plane then it will turn clockwise in the yz-plane because of the gyroscopic effect. If you have a wheel spinning the opposite way, and if you turn it clockwise in the xy-plane then it will turn counterclockwise in the yz-plane because of the gyroscopic effect. Adding the two effects cancels them.