I'd use propane for leak checking. As to idle, I'd try for the leaks first and if that doesn't do it, go for the next things. Get MAF cleaner and clean the MAF and the throttle body especially the IAC. If that doesn't cure it, take the injectors off and have them sent to
CorvetteInjectors.com for a cleaning and testing. I don't like to try clean them since you have no clue as to what the injector is really doing as far as it working and how well. IIRC, $15 per injector so it isn't too bad if you are going to keep the car
Does it do it in cold startup or warm idle?