I doubt you have bad injectors-- LLY engines do not eat injectors like the early LB7. Mechanics replace them-- they make good money and are easy to do on a LLY-- or they don't know what else the problem can be, and hope that will fix it.
The FICM harness does short out, and it will act like injector problem, also the injector can have loose connector, and cause problems.
First, check for codes. Also read the rail pressure when cranking.
Chevy 04.5 LLY, 2X, shell, XDR, MikeL Heavy duty up-grade, 6spd, TransGo, deep pan, de-badged, 65 Gallon replacement Aero tank, LBZ-mp, Kennedy pump, shimmed, Pre-fuel filter, tow mirrors, BU cam, gauges, GPS, Sirius, bags, custom grille, fender vents, HD trans cooler- Curt front hitch, footwell lights, load lights, Studs, head gaskets.