I have a mess on my hands 06 Grand Marquis

I bought a 110,000 mile, 06 Grand Marquis with known issues really cheap.
It bogs on acceleration under load... Falls on it's face and stumbles but idles fine and revs great.

The wrench in the works is it has a custom tune on it with a cat delete pipe installed with flowmasters so I felt like this is the root cause of my issues but have mechanical anomalies I want to get sorted first.

Mechanical fuel pressure test by the fuel pressure regulator - have a "bouncing" 28-35 psi (~40psi on scanner with the pump running at ~17-30% capacity according to my scan tool). Mechanical gauge shows 50psi just after the fuel filter, almost directly off the fuel pump. Is this enough PSI? So the car bucks and barely runs with throttle, under load (and the fuel pressure dips) - but then when you disconnect the fuel filter, drain and reconnect - the car runs fantastic for a few miles before the symptoms start to creep back up. No obstructions that I can tell in the fuel lines - air flows fairly well through them.
So I was wondering if:

The PCM/ECM controls the fuel pressure since it's a returnless system? I've disconnected the fuel pressure regulator vacuum line and even the electrical plug and no real change in symptoms. It baffles me that I can drain the fuel filter and then get it to run relatively fine for a while - is it possible some cavitation or something is building up in the lines?
Is 30psi enough at the [self installed] shrader valve?

I only bought the vehicle because its so low miles and it was a steal - I could recoup my money just by selling engine/tranny easily - but Id like to fix it.
I initially, and still think that since the cats are deleted and some unknown custom tune has been installed that this is the root of all my issues - and I cant detect it on my scan tool - the computer is fooled. I do have codes in every module - so I was thinking if the PCM controls fuel PRESSURE then I have a computer/tuning issue rather than a physical faulty new fuel pump. This one is scratching my head - I wish I could have the stock tune put back on and just deal with the codes for lack of 02 info - at least Id be able to diagnose the issue.
Im thinking I really need ~40psi at idle at the rail - but dont understand why the issues go away when I disconnect the fuel filter??

Any ideas?