Wouldn't that be a short trip that entitles the cab to go straight back to the terminal to pick up another fare instead of having to sit in the feeder park first?

A quick look at the schedules suggests that the OP should have at least 3½ hours in which to do this, so if all is running to schedule there shouldn't be any need to stress about timing. If the inbound flight to LHR gets delayed, then the OP knows the progressively faster options.

Presumably an airside transfer could start with getting the bus from the T5B bus stop? (I see the connections guide is already linked to from the signature in KARFA's posts.) Could that save a bit of time, even if there is then a change of buses because of the current arrangements.