To me it sounds like perhaps both air intrusion And a couple bad glow plugs.
1) Take a few minutes to ohm test or test light each glow plug while it is unplugged from the wiring harness. You should see some resistance if using a ohm meter or a dim light if using a test light. You may have 1, 2, or 3 dead ones. Also look for problems with your gp wiring harness and gp connectors.
2) Air intrusion causes different start up issue symptoms.
a) Longer crank times.
b) Engine that races up after several cranking attempts, which is the extra diesel that made it to some cylinders when cranking for a while burning off. Then comes the cloud of white smoke which is not fully burned diesel.
b) Engine idles rough, till it primes.
c) Engine idles rough and then dies 1 or 2 times. Does this a couple times till you achieve prime.
3) You mention more clatter, you likely know, but when the engine is cold the IP advance comes on and causes more clatter.(Advances the timing.). But also check your cold start soleniod is working and raising your idle, that will help too.
So if your glow plugs test 100% now you will need to find the source of the air intrusion.
Attach some pics and let us know what you find.