K-Jet Idling troubles on initial startup

[Vakito]

Hi All, I have a 1988 240GL with a B200E K-Jet engine

The engine runs sweet as a nut once it's up to temp but there's a couple of problems when first starting it up/running cold.

First one is tricky: The engine fires up instantly in all conditions which is great. However the engine is really lumpy as soon as it fires up and can last anywhere from 3-15 seconds. Feels like the engine is firing on 3 and sometimes 2 cylinders only. I usually rev it up to 1500RPM for a few seconds, still feeling lumpy and suddenly the engine will go smooth and give flawless performance until next startup. Sometimes if you don't catch it with the throttle in time, the engine will stall itself and takes a while to start back up because the initial pressure from the accumulator is gone. What could the cause of this be? Injectors, fuel pump, fuel distributor?

Second problem is simpler: The engine idles at around 1000RPM on cold startup due to the aux air valve but after about a minute the idle speed drops to around 5-600RPM making the engine very lumpy, equivalent to pushing the choke in too soon on a carburated engine. To counter this I have to manually bring the revs up to around 1000 with the throttle while at a standstill. The idle speed will slowly improve as the car warms up to the ideal 900RPM when it's fully up to temp. I've read somewhere that the aux air valve takes around 8 minutes to fully close. Is mine closing too fast and needs replacement?

Cheers
Peter