It is important to note whether the problem is a single cylinder misfiring or whether it is random misfires. Any idea of air in the pump chamber would be random.
If the misfire is a single cylinder a likely possibility is a fuel column leak down. This can happen either from the injector (into the cylinder slowly over time) or from the internal sealing of the pump element check valve (the fuel leaks back into the pump body and can't be detected except by symptom). In either leak the engine starts without fuel in one (or more) lines. It takes multiple injection pulses to refill the line, thus taking a while to run.
Our standard service for such problems is to remove injectors, bench test for leaks and spray pattern, check engine compression, verify visually the glowplugs (and carbon build-ups)through the injector hole, and reseal the pump element check valves.
We do the compression first as thats the other reason for a cylinder misfiring on start-up.
Bosch Master, ASE Master, L1
33 years MB technician