I don't think this is anywhere near as complicated as you make it sound.
IF BE (or anyone else) were contracted to fly to LGW and back x times a day, at specified times, then any mx cover etc, for the regular (liveried?) aircraft would come from the main BE fleet. It would be in the contract.
It's what happens with the current BE/Brussels Airlines contract.
It's what happens with the arrangement between T3 and BA on IOM-LCY.
It's what happens with contract flying, the World over, every day.
It's effectively what happens now with the current BE GCI based E175.