[LS short box]

Haven't used the CPP 255 kit. But I'm guessing it's 255 Walbro fuel pump. I've used them on a number of LS swaps. My 98 Wrangler LS6/4l60E has used one for over 15 years and is still going strong.
Make sure it's a "real" Walbro.
I don't see how the tune will affect the fuel pressure. The injectors may be an issue but you have to get the fuel pressure down to 58 psi at the fuel rail.
What are you running for fuel injectors? Again fuel injectors bought on-line can be a total mess not unlike FFR's.