Our first aim is not to blow up at project demo, i.e. next week

So, there wont be any bump surfaces... Then we can agree that there is no need of suspensions, right?
I was about to ask that problem which you explained. When load is lifted center of mass will shift to front side. So torque values at front wheels will be greater and of course this will cause a reduction in speed at front wheels while back wheels are still rotating with same speed. When this happens, there is no problem in forward or backward motion. However side motion -just like you said- will be irrelevant. About that, we couldnt find a solution. I have watched some videos with huge frames running with mecanum wheels. And clearly, the weight was not distrubuted to each wheel equally! How come they dont fail?
In short, when torques of wheels are not same this will cause different speeds. However same speeds of all wheels are needed in order to get a straight line. How can we manage that?