Thank you all for you your feedback, but I'm afraid most of the obvious ideas have already been checked.
We are testing the wheels now with no weight on them at all. I can easily tell by looking at the wheels that they are not spinning at the same rate. All gear boxes came from the Andy Mark upgrade kit so they all should have the same ratio (all the gear boxes do look identical inside). We did grease the gear boxes.
We are using Jaguars. My feeling is that the problem is mechanical rather than electrical. We aren't using the Mecanum drive code (with the Java WPI Lib) right now, we are just running full power to the motors or whatever we get from joyStick.getY() input.
Here are a couple of pictures for reference:
top view of control system
Wheels without wires
Do Jaguars sometimes develop an issue where 100% power really means 80% power because the Jaguar is failing?