Probably the best fajitas I have ever had was at "The Roundup" in Pharr, the lady who owned that place has been credited by many for being the first to commercially promote "fajitas". Her marinade and her method of cooking was incredible. Papasitos and all the in vogue places couldn't carry her jockstrap.
Not one piece of fajita at The Roundup was ever grilled. All were seared on a very hot flat top, basically done in the Mexican "A la Plancha" manner. Which means that with a good cast iron skillet and some heat you can have excellent fajitas, I prefer them done this way than grilled.
It all starts with the meat. If you can't get skirt steak, ask a local butcher for "hanging tenders", which is the "arrachera" cut from Mexico. Butterfly it, marinate it Italian dressing (the base for The Roundups marinade and why so many Valley Rats use it), some soy sauce, lime juice, and maggie sauce if you can get it. Dust with season all or fajita seasoning and hit on both sides for a couple of minutes in a cast iron skillet, add some onions and japs towards the end of cooking and you are golden.
Butterfly the cut of meat so it is thin. This will work and it will be good.