The Pump is driven by the engine gearbox, which in GE has its own heat exchanger interface with fuel. The HP doesn't pump a great deal more than the engine requires, and the spill is a fairly closely calculated flow that is more a safety consideration than a potential Gross Tankage circulator. EPR is Fuel reliant directly; the 'Safety' factor not even a critical one, if the fuel isn't enough, the engine keeps running, but at a rate that is flow dependent, as BA038 demonstrates. What's critical is to keep the Flame lit, and not add too much fuel.
All I can do is repeat that Water needs to be out of the Fuel. Including the mystery water that comes from secret places that are mysterious and cause unknown boffins to build imaginary 'test beds' that keep the public distracted until they lose interest. Why heat fuel when sumping and caution are enough ? I say we make them choose; frankly I'd choose better Fuel supervision, but that's me.