>forced to do drills for a day in mismatched shoes while singing
My feet hurt just thinking about it...

Anyway...
>"Mind if I take a look at the axle? A fresh set of eyes never hurts to have around."
We could try making the cart into a sort of sled by replacing the wheels with runners made of tree branches or less necessary planks from the cart itself. Hopefully our tools include some nails or tent stakes to fasten them. Picrel is what I'm thinking of.

Another option is to rebalance the weight of the stuff in the cart toward the rear so the rear axle takes most of the weight.

Final option I can think of is to make the cart into some sort of trike.