More thoughts --- seems on further checking I actually have 4 Bosch K-Jetronic books (where did I get all this stuff?
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A little reading leads me to believe that my problem on my 82 SC (which I think is identical to yours) points to the warmup regulator. The manual seems to indicate that the Cold Start in combination with the Thermo-time switch is really limited to only the first few seconds (maybe 10 or so --- it's not real clear on the length of time) of the startup period. Since mine and, I think, yours, starts instantly every time (mine does, no matter what the weather) but then coughs and spits for up to about 4 minutes afterward (depending on the weather) the manual seems to point to the warmup regulator as taking over during this period of time until the engine gets up to full operating temperature and warms up the walls of the intake tubes and cylinder walls so that the right fuel mixture now reaches the combustion chamber and everything runs right. The Warmup regulator also works in conjunction with the Auxiliary-air device (haven't looked in mine yet to see if I have on of these though I remember one on my 74).
Anyway, that's what I can offer without just copying the whole book in here (can't anyway, you know, copyrights being what they are and all ha ha
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Good luck and let us all know what you find.