Incidentally I too changed a load of stuff with the first pump trying to fix it (timing chain, hydraulic tensioners, glow plugs, wiring to plugs, injectors and more, all to no avail). The missing/clatter with the old pump at cold idle was random, not every time one cylinder fired. It would go purrrrrr-clack-pur-clack-puuuuuuuuurrrrrrr-clack if you see what I mean. Each "clack" would give a puff of unburnt fuel from the exhaust. My new pump doesn't clatter much at all at cold idle, the clatter comes from driving it while still cold.
I'm convinced it's a timing thing that would go away if I adjusted the pump timing, however I'm reluctant to do so because a) it runs fine when hot and b) I'd rather find out what causes it in the first place