Hi, I hope I've been able to help. Remember, if the cylinder leak-down test shows the rings and valves are in good condition, the problem is most likely with the VVT system. Also, double-check the spark plug code, as these types of engines have slightly longer spark plug electrodes than standard ones. If, for any reason, you can't perform these tests, another option is to program the engine idle speed. You should do this using a Tech2 programmer and program it to idle at 1000 RPM (this would be a temporary solution until you repair or replace the faulty components). I guarantee it will start much better when cold, although the idle will be higher. This option is an alternative, not a solution, but it will greatly improve starting. When the VVT fails, one symptom is very difficult starting or the engine won't start at all, but once the engine warms up, it runs perfectly.
Try these options and remember to let me know how it goes. This problem is very tedious, so opt for the second option if they can't diagnose it quickly. Best regards, I hope this helps with your problem.