I'm definitely not an expert.
But reading here, there is a pattern among some of the non-starters.......
Fuel dripping and "we leave it, have a cup of tea and away it goes"
I've only twice ever seen fuel drippng from an aircraft. Both times were my fault and the flooding resulted in a failed start.
I would definitely be experimenting from a directive of a much lower amount of priming.
Talking (in my experience of engines with priming done on the throttle),
all lycomings I've started needed only 2 or 3 throttle pumps regardless of how cold the day was.
While cranking, gently opening the throttle, but ready to catch the start to prevent the enging bursting into life and straight into roaring at 1600+ rpm.
Occasionaly if that wasn't rewarded with any life, (maybe 5 or 6 blades)
Then 1 or possibly two more pumps.
If experimenting results prove more is required, then perhaps the pump seals are shot and its only resulting in the same volume of fuel as a good one?
Obviously some guys on here have much more experience and knowledge than me but that's how I see it.