The EFI compensates the injector timing on the voltage it gets, so I think that is one (of many) reasons the EFI wants a connection close to the battery. With a kill switch, I would run a separate circuit through a relay that is activated by the kill switch (and maybe the ignition key too.)

With all the warnings FAST has for their EFI to connect directly the the battery, I'm suprised they don't supply a large capacitor to be installed?