I'm not sure if (independent) bracing at the front and rear is going to help much. It'd reinforce those elements to be more rigid transverely but it still won't help torsional rigidity (twisting between the front and rear suspension elements) or longitudinal flex (bending between the front and rear - what you seem to be describing when you talked about parking the car on a curb) in the overall chassis.
What you need, is a brace that ties the front and rear elements together. Without looking at how the car is put together, I'd say have a look at the transmission tunnel and see if there is enough space there to fit a member here. Or you can reinforce the floor pan.
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