My approach on your symptoms as with most diagnostics is to understand what is supposed to happen and monitor the condition looking for pieces that are deficient and fit my hypothesis of how that part doing what the test results show causes the events as they unfold.
In the simplest of terms I would wish to know if fuel mixture, spark quality, or various timing elements were the cause.
A fuel explanation could be as simple as this: A rich mixture facilitates cold starting but overwhelms the warm-up phase. As lambda takes over the fuel system mixture is compensated for and again runs OK.
Some set of events of this nature or of individual nature (cylinder to cylinder) will be involved if mixture is involved with your problem. Basic mixture, improper fuel pressure control, air flow plate base centering, fuel distributor base settings, injector flow problems all can mix to form variations of the problem.
I would remove the aircleaner and have someone start the senario you have described. As the car starts to run bad slightly push the air flap down or lightly pull up. By doing this one can make quick evaluation of whether fuel is the cause of the problem. Doing such causes the base mixture to be changed up and down. Single cylinders with flow problems can be corrected by adding more fuel to all. The rich ones do fine untill some point where it they start dropping because of a rich mixture.
Use your knowledge of what causes what to change the situation untill the general cause is detected. They use simialr technique to zero in with further testing. The above test can specify or eliminate fuel from the equation in a few minutes with no tools.
Just remember that since you have never done this your judgement will be poor. Everyone owning a K-jet car should learn this evaluation technique by observing the general reaction and more specifically the electronic reaction on a closed loop situation on a functioning car.
Bosch Master, ASE Master, L1
33 years MB technician