Inverted installation affect idle?
99% of pattern airplanes use inverted installations and those guys have little if any problem.
The reg screw probably needs to go out. Start with 1/2 turn and see if the problem improves. You may also have to close the air bleed. Try going back to 1.5 turns open as a start.
ONCE AGAIN, THE REGULATOR DOES NOT CHANGE THE FUEL PRESSURE!!!!!!!!!!!!!! IT is a demand type regulator which you adjust to give the engine more or less fuel, DEPENDING ON THE THROTTLE POSITION!!!!!!!!!!!!! Think of it as a mid range needle.
You did not mention plug or fuel, what kind? The prop should not make any difference.