I own a 2001 P38 4.6 HSE and had failure codes for the Oxygen Sensors and maybe some other components, can't remember exactly, for several months. I resisted changing the Oxygen Sensors and started to read all and any LR forums for related failure code clues.
The true failure was the Mass Air Sensor. A dirty Mass Air Sensor does not read well, all I had to do is spray the Sensor wires with a solvent to clean them. Problem solved without replacing any parts. The hardware/straps securing the Mass Air Sensor had non standard tools making disassembly to reach the internal wires difficult. Could not remove the MAS to clean it, so disconnected the duct work elsewhere.
You replaced the Mass Air Sensor and the problem persists. I bought a NANOCOM engine analyzer ($500 US Dlrs) to help solve the Oxygen Sensor false alarm. Convinced myself that the OS were OK and the problem is elsewhere.