For strength, triangulation is your friend. Along the sides, I would put a diagonal in all 4 sections. As far as the front goes, I would put diagonals in both directions, hence making an "x". I would also "x" the 2 sections behind that. That is a bit tall and narrow to do less than that, in my opinion.

This is all you need. The red follows the front plane and the green the right plane.

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At 4000 lbs you are looking at roughly 1000 lbs (~ 500 Kg) per wheel. The front wheels, supported by 6 posts each, seem sufficiently sturdy to me. That's less than 100 Kg per post. What I find particularly worrisome is the far end where you have about the same weight and only 2 supporting posts. If anything goes bad it will be at the far end. Your greatest enemy is the buckling of one of the columns. I would suggest adding supports at half height between the columns to prevent that from happening. Google "eulersche knicklast" for inspiration.
Looks to me the entire structure should be turned upside down.

The green in the front is good. Prevents the columns from buckling. The red keeps it from tipping sideways. Still, the ones in the back are what concerns me the most. Some kind of additional support in the back, from top to ground would be helpful.

As a simple experiment, take a drinking straw and press on it until it buckles. Then cut it half length (or have someone holding it at half height) and repeat the experiment. You'll see that it takes a lot more force before the straw buckles in the middle (Knicklast).

That's pretty awesome!