The hydroboost system is its own separate system so the only thing that could make the car just die under heavy brake load is excessive accessory drive drag which unfortunately you can't do anything about. One thing I have noticed though is how Ford uses the tee line that connected the low pressure output of the hydro as well as the low pressure output from either the cooler (or the rack output if no cooler is present) back to the reservoir. It creates a restriction that can impede flow from reservoir back to the pump, quite possibly cavitating it and creating the excessive drag which would starve the system of the hydraulic power it needs. In other words, something's gotta give and with the amount of output those P/S pumps are capable of outputting (I think somewhere around 1250 psi max), well, there's the answer.
If you're using the stock reservoir, there's nothing you can do. But with a system as pictured here, you can run separate return lines which should in theory eliminate the restrictions. I have yet to test this out though, but hopefully I soon will be.
The big line is the gravity feed to the pump while the two smaller ones are returns from hydro and the cooler.