You’re confusing me. What kind of vehicle is this? If you have an idle mixture screw it would be carburated, but you are asking if the EFI computer is going to adjust something. What is it you are fooling wiht, because if you have EFI there is no such thing as an idle mixture screw.
You claim you cannot set the timing to stock, yet say you have intentionally advanced it thinking you will get more performance. If you can intentionally advance your timing, you can intentionally put it back to stock to.
Changing base timing, timing curves and air/fuel mixtures is what we used to tinker with to try to get more power out of cars built before 1986. With EFI, if you alter the base timing the computer is not going to like you for it and will not give you better performance but instead it will be worse. They computer also has full control over your air/fuel ratios at idle and every other speed by varying the pulsewidth if its injectors. Short of reprogramming the PCM you cannot alter it. Hence, you cannot change your idle mixture. Nor can you change your timing advance, as once again it is controlled by the PCM not by centrifugal weights or a vacuum advance mechanism. Those have gone the way of the dodo.
When asking others for help with a vehicle they do not have in front of them to see, it would help to tell those people important information such as the year, make, model and engine size of the vehicle. Also worth noting would be the mileage on the car and a detailed description of the issue you are having. If it only started after recent repairs were made, tell us that. If it only does it before it warms up or only after it warms up, that would also be needed information to help narrow down possible causes and develop a strategy to take with diagnostics.
Please help us help you.