define "running bad"
the OEM fuel system SUCKS fuel from the tank, your pump pushes it, if your add on pump isn't supplying the needed volume it is now an obstruction in the system, causing greater resistance for the CP3 to draw.
Fuel filter(s), new? clean ? seated properly ? bleed screw on filter housing tight, not cracked ? WIF sensor on bottom of filter fit properly ?
LB7 is known for injector issues, any fuel in the oil ? has it set any codes ? if an injector is bypassing, it will cause overall fuel pressure to drop, which could act like a fuel pressure regulator problem.
Need a scan tool to see actual and commanded fuel pressures, if it will reach 23000 psi when commanded, but then it drops off suddenly, yes, then I might suspect FPR or even the injection pump, but there are several other things it could be.