K(E)-Jetronic usually suffers from different hot start issues, cold start problems are a little bit harder to find.

As it's running fine when warmed up and also starts fine when warm (does it really?) I think there's no problem with fuel pump, fuel filter and the mechanical parts of the metering head.

How old are your injectors? Mechanical K-Jetronic injectors suffer from wear, older ones won't seal properly and start to drip when the engine is turned off. So the next morning your cylinders are flooded and the metering unit will take some time to get fuel into the lines, build up pressure and start the engine again. When your injectors are older than ~75k miles it might be a good (but not cheap) idea to replace them.

First thing I'd check is the auxilary air device. Take the hoses off and you should be able to see through a ~4 mm big hole inside. when you can't see through or just see a very small hole, soak it in brake cleaner overnight and then try to move the stuck plate inside with a very small screwdriver.

Second thing is the cold start valve. Take it off the inlet and check if it works for several seconds (8 iirc) when you start the car from cold.

Third thing is the water temperature sensor below the inlet manifold. Check the resistance of the sensor when the car is cold and when it's warmed up. Should be different. Someone here should know the exact values.

Fourth thing is a little bit tricky. It could be the ECU or the hydraulic device on the side of the metering head. Try to find the problem by testing the given fuel pressures.