Two simple rules come to mind.
Landiing clearance should not be given until the active runway is free of ALL taking off and landing traffic.
'Position and hold' or 'line up and wait' should not be allowed, aircraft should only be cleared for departure from the #1 position at the holding point short of the runway.
If it slows thing's down, so be it.
I would prefer to run the risk of 'blinding' other pilots with strobe lights than being on the runway at any time without using them and 'disappearing'
If they bother you, look away, you are being noticed and that is a good thing.