[Leav]

Perhaps you could implement a control system which compensates for traction loss caused by un-evenly balanced wheels.

It would not be easy but it would be perhaps easier to implement a basic control algorithm then building a chassis, bases on your personal capabilities.

Just reread your post.

You should be able to mount all 4 wheels no problem to the chassis at the same height.
Regarding the drive: if you are going for a simple drive like you mentioned perhaps you should in fact implement a PWM, and experiment with different values for the motors to achieve a balanced motion.

for example if more weight is on the front wheels you would only give them perhaps half the power when going sideways:

front_left=50%
front_right=50%
back_left=100%
back_right=100%

to get a straight line.

this will, of course, only work on flat surfaces. any bumps or irregularities and you are back to square one with the need for a suspension, like Eric mentione.

Good luck!

-Leav
(Israel)