You don't necessarily need the coefficient of friction. Just measure the force to move it across a level floor. The frictional force pushing it up the ramp will be just a tiny bit smaller, since the normal force will be reduced very slightly due to the very small angle. Assuming the force to push it across a level floor isn't too large, the difference is insignificant for what you want to do. Plus, some of the components that make up the total friction would be independent of the angle of the incline (e.g., if the bearings are in a very viscous lubricant, merely spinning the wheels, regardless of normal force, is going to have a frictional force.)
So, merely calculate the weight of the rack times the sine of whatever angle it is, and add that to the frictional force pushing it across a level surface. Actually, you don't even need to calculate the angle, since the sine of the angle is 8/sqrt(122^2+8^2) for one of the ramps, and 12/sqrt(156^2+12^2) for the other ramp.
And, fwiw, I believe the frictional force would drop to no less than the cosine of the angle times the frictional force over a horizontal surface. That is, 156/sqrt(156^2+12^2) times the frictional force on a level surface. Or, 99.7% of the original frictional force. The other works out to 99.8%.
For those thinking coefficient of friction really mattered though, you're probably thinking static coefficient of friction. You're not doing work against the static friction though - that's what's making the wheels turn rather than slide. E.g., you can walk easily across a floor vs. walking across ice because of the static coefficient of friction, not despite it.