So. No underbonnet LP pump on that year.
There is some debate as to whether that year has an in-tank pump AND a LP pump behind the OSR wheel arch, or just the LP pump behind the OSR wheel arch.
Either way, it could be that your LP pump is on the way out.
The other possibility is the cam sensor, although this tends to show as faulty more on hot starts, but isn't unknown for cold starts either.
You say you have refurbed injectors - still worth doing a leak test to eliminate them.