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It sounds like you have what is becoming a common problem with the later 6.0l engines. The FICM(fuel injection control module) is failing,Ford claims that all the calibration updates that have been downloaded into this module have damaged the internal voltage regulator and when it is cold the module cannot supply enough voltage to operate the injectors properly.To repair you need to install and rpogram a new FICM.
Yes it could be either of these,the fuel pump needs to be physically tested for pressure and restriction, the plugged cat can be checked by checking the EBP pressure with a scan tool,with the truck in park the engine running at wide open throttle the pressure should never be over 36.5psi.