Most of the flip fronts I have seen don't seem to have any bracing from front to rear
It might be that the fronts are fibreglass so don't need bracing. Steel will be a bit heavier.
I'd take a guess that the Mini wings and engine bay sides actually provide a bit of structural support so it suprises me that that the subframe doesn't just rip itself out of the bulkhead once these are removed.
I presume that you need a diagonal strut from the front of the subframe to the body at the top of the shock tower.
Never seen it done though!