All you want is positive pressure feeding the CP3 to get the benefit. It doesn't matter if it is 1psi as long as it stays there under WOT.
My Airdog 150 (older model) holds 11-12 at idle, and on the dyno at WOT it drops down to 2-3psi.
I would like to run a higher volume pump (gph), and keep the pressure low. The lift pump is there to supply the CP3 with fuel. Fuel does not compress(appreciably) so you do nothing trying to force more psi to the pump(except piss it off). You want to stay above 0psi so that you do not create a vacuum in the supply line and risk cavitation.
If you have rail pressure issues, increasing the CP3 supply from 5psi to 10psi isn't going to help you.
What he said.
The only reason to run higher pressure is so at WOT your cp3 gets positive pressure to it. 5psi across the board at idle or WOT is enough to be a good maintained pressure (so long as it's steady pressure meaning the flow increases as needed to maintain 5 psi. I use 5 as a buffer to account for any sudden momentary drops in pressure. Positive pressure is the key word.)
If you have a steady 5 psi then your flowing more to the cp3 than is required and if your still losing rail, you need more cp3 plain and simple. Pressure is just a resistance to flow.
As previously mentioned, running higher pressure on an LB7/LLY will NOT affect how the FICM works. However, you can crack the circuit board, or blow the seals out. If you went high enough, you could probably blow up the case too. It's just aluminum and not originally designed to take ANY pressure.
What is affected is the FPR on the CP3. The spring and current flow at stock settings cannot regulate very well at higher pressure causing surging which results in a lopey idle. You can raise the current flow in the tables to compensate somewhat for this, but don't expect your FPR to last as long. It will run hotter and likely fail sooner. And this is inherent to all common rail trucks using electric flow control. (FPR)