All the cold start functions are part of the "E" portion of the system, so if you disconnect it the car won't cold start. You can test this by removing the OVP relay, which provides power to the various "E" portions of the system and the ABS computer. See for yourself - remove the OVP relay and try to start it cold.

If the duty cycle and EHA current are in the correct range, then your problem is somewhere else. Disabling the "E" part of the system is not a viable course of action.

Did you ever check the TVS and CIS temp sensor?

Duke