David you should run a wet kit since you already use all of your available injector pulsewidth. A single fogger jetted to 40-50hp is a good start. You should tune for low 11's A/F when you're on the can. Be sure to mount the nozzle after the mass air meter. Try to always run the same bottle pressures since higher bottle pressures will increase the amount of nitrous entering your engine and altering your a/f ratio and lower pressures will cause to run too rich and may bog the motor.
Start spraying above 3200rpm and only at WOT or you will have bent rods. Too low of bottle pressure may load up the engine and backfire causing bent rods.
The LS should have a WOT switch behind the gas pedal that the stock ecu uses. That switch probably sends a ground signal to the ecu when the it's pressed. You can tap the wire going into the ecu for your negative relay trigger.
May be a good idea to use a diode on the negative relay trigger wire as the ecu may freak out seeing a load on what should be a 0v input, although i have never had a problem on supras. Maybe your split second piggyback has a rpm based trigger, otherwise you will have to use a window switch.