2005 F-150 Lariat 5.4L 3V

Any ideas what could cause hesitation on moderate to heavy acceleration and will occasionally backfire through intake?

New motor, intake, TB, coils, air filter, fuel filter, injectors, MAF, TPS...

Is currently in shop, mechanic having hard time finding problem. I cleared CPU to do full run cycle after new TB install (fordtechmacluco suggested to do after TB).

I also think it should have more power than it had. Mechanic wonders if timing incorrect on remanufacture, but I'm not sure as it runs very smooth at idle and cruise and does seem to have more power at times.

I really think it if fuel/air problem... I used after market intake (doorman) and TB (not sure of brand). While I don't think the intake is the issue, I suppose it could be the TB. I HATE that the fuel pressure isn't easily verified, but I don't think the PCM is that far off with the actual pressure, as I am sure I'd see a code for something.

only about 7k miles on new motor.