3.8 motor with supercharger missing while idling runs rough

Yes, take a compression check of the engine to see if base engine compression happens to be low on cylinder 4.

IF compression and spark ok .. Test injector pulse using noid light - if injector is accessible .. You can also use stethoscope (LONG screwdriver) to listen for injector clicking ..... Next choice is have an injector balance test performed at local repair shop, involves a pro quality scanner and fuel pressure test kit... Misfiring injector will mimic ignition misfire! .. New injectors does not necessarily mean all of em are working properly. https://repairpal.com/repair-shops