Like I said earlier take a look at your gear ratio.
I think there are going to be more than a few teams not getting the performance they should due to using the kit bot gear boxes without changing the ratio. The ratio selected was based on a 6" wheel not 8-8.5 that I have seen teams say they are using.
I thought your analysis sounded familiar to something we experienced back in the day. Besides having only the 4 corner wheels on the ground with that chassis, there was a lot of friction in the chain routing/tensioning. You could have fried an egg on those motors by the time we got thru the playoffs at MSC.
Another thing to think about with this setup is what actually is taking place while you are scrubbing the high friction tires in a turn. You will subject your bearings and other drive parts to exceptional side loads which in turn raise the friction there as well. With all of of this increase in friction, you will send the motors into a near stall condition which will take you to somewhere north of 100 amps per motor. Depending on your electrical design, the electrical loss could be significant and therefore reduce the available current to each motor. If one side has a much longer wire length than the other side, then turning in one direction may give you half the loss that turning in the other direction might produce.
What Dr. Joe is alluding to is shorter wheelbases will reduce this side friction as you turn. You may get a better handle if you were to draw the force vectors encountered in a turn for each of the wheels. The wheels closest to the center of turn will have the least side force which in turn produces the least (relative) electrical load.
A fully charged and new battery can supply up to 600 amps but not at 12 volts. Typical batteries may only produce 500 amps for the beginning of the match but much less towards the end. Your mileage will vary on final ratios, size of tires and where on the motor curve you have chosen to run.
If you’re committed to this layout, and you’re using one chain per side as is most common, I suggest putting the CoG significantly towards the axle which is not coupled by chain to the center wheel, and note that you will get your best acceleration away from that axle.
Try to find some way to increase the center drop. As I noted above, recall that the center axle is already a dead axle; don’t be shy about using cover plates, putting a bolt through them, and mounting your wheels on bearings to accomplish this.
The team had already bought the nano tube for our air cannon before I became seriously involved. Looking at it later, this seems to me to be a great way to mount mecanum if you can get the right gear ratio, but for anything else it leaves much to be desired.