It really sounds to me like either a fuel-delivery issue or an idle control issue. When the car is cold, there is a different idle speed the idle control holds the engine at, usually just 500rpm above normal idle. To me the numbers you're describing sound way low, like the idle control is set 500rpm too low. I don't know for certain, but that's an idea you can look into? You could also do a fuel pressure test, just find a pressure gauge you can attach to the fuel delivery lines and turn the key in the ignition to the on position without starting the car, should cause the fuel pump to run and you should be able to check the fuel pressure readings that way. I don't have an inkling of what proper fuel pressure is for you though, so you may have to look it up, or ask around.

I hope you get all these problems sorted soon, otherwise you're going to be flintstoning that del Sol.