Starting and idling problems

I assume you have headers on it. One nice thing about that is if you let it run a little like in the first video you can quickly touch the header tubes and make sure they are all getting equally hot.
If you had one not getting hot that would indicate a problem in that cylinder. You could have an injector not flowing enough or even leaking down .
If you don't have complete confidence in these 5.7 injectors , it may be time to put new ones in it.
You could even get a hold of performance shop like Modern muscle and see if they would have a good set, I am sure they upgrade to bigger ones a lot and have good stock ones off a running vehicle.