I would assume you would burn the higher speed motors as they will try to drag the lower speed motors forward.
I was able to get 4 of the same motors. It took some time as the motors are not officially for sale, but parallax worked with me and sold me 4 new ones. I had 2 older ones, but they are slightly slower and you said I could not use two fast motors and two slow motors. So it took some time for me to convince them that I need 4 sets as they don't have many ready.
Think about it a bit: We are talking 4 wheels here. If you moved the wheels in the front back, and the ones in back forward, until they were near the center (but still spaced opposite each other), then yes, it would be easier to turn. Heck - if the wheels "merged", then you have the classic differential steered robot (add some casters on the front and back to balance).
I was thinking about putting one wheel/motor on each corner of the robot but you explained how that would screw up the turning.
What if I slid the wheels from the corner down towards the middle of the robot so that they were almost touching and then put a caster wheel on each end of the robot. It would be like putting two, three wheel robots back to back. That way the driver wheels are like .5in apart making the turning easy yet the caster wheels will help support the front/end.
Would that work? I think it would yet I have never seen a robot like that.