Where is the MAP sensor located?

The 5.4 3 valve in those doesn't use a MAP sensor, they use an integrated Mass Air Flow and Intake Air Temperature unit instead.

What is the issue or code you have that suggests a MAP sensor problem?

Have you checked codes?

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

Thanks

Just to jump in, do you have a check engine light or any warning lights?

It is probably a good idea to check for codes just to be sure we don't have any.

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

However, it sounds like you are having an issue with the fuel adaptives.

This is most likely caused by o2 sensor issues because what happens when you clear the battery is you are wiping the memory of the PCM.

Then it takes about 100 miles to run through all the required monitors and then it starts using all these systems to optimize the fuel consumption.

The best way to try and figure this out is to monitor the o2 sensor data with a scan tool but I know you don't have one. Does anyone you know have one that can monitor o2 sensor data?

Basically, I think we are going to be at a stale mate if we can't start monitoring these systems to find out where the issue is.

It may not like aftermarket parts, many don't these days. However, the likely reason is that the replacement is out of spec. With the quality of parts these days anything can happen. However, it sounds like the issue is with one of the parts that does require a drive cycle causing a problem, like the O2 sensors or possibly the MAF although that would usually show problems without a long drive cycle. How does it start after you fill it with gas? Short crank time or does it take a while? Is the engine quiet at idle? Any rattles or ticks? The 3 valves are bad for losing rocker arms. That shouldn't cause poor MPG, but it could cause an erratic idle if one is failing.