it is not a weak CP3 pump,i have had this happen to my LBZ sevaral times and heres the most notorious ones..
weak FRV(Fuel Rail Valve),how to fix is either replacing with stock,putting a shim kit in or a race valve in.
Injector Control Mobule Harness,if it is bad it will cause stuff like that also.
Project, Rogue Budget(Workstock Puller)
2006 GMC 2500HD, Stock Motor, EFILive by me, Billet 63 VVT, Motorsport Stroker CP3, 20% Nzls, ProFab Manis n Uppipes, BD IC, Hot Pipe IC, ProFab Y-Bridge, lots of other goodies