You mention they replaced the MAP sensor, but I believe you have a MAF sensor (possibly in addition to the MAP). On the v6, we have two MAP sensors and two MAF sensors. Not sure what you have on the V8.
MAPs are in the intake manifold and measure the intake pressure, MAFs are in the intake plenum, usually not far from the air filter box someplace, and measure intake air flow. It’s usually the MAFs, not the MAPs, that cause problems. If they replaced the MAP, but not the MAFs, you can try replacing or cleaning the MAFs to see if that helps.
The other thing you might check is engine coolant temp sensors. If you can see actual engine temp on your generic scan tool, check that first with the engine fully warmed up. I believe the v8 should be around 190-200 F if I remember correctly.
Then I think o2 sensors would be next on my list.
The other thing that might help is resetting engine adaptations, though I’m not sure how you do it without a GAP tool.
Another thought - could be exhaust manifold leak.
In the end, you might spend more money chasing this down by replacing parts than just taking it to an LR shop for diagnosis first. This is especially true without a scan tool because you really should reset adaptations (or drive a long distance) after replacing each part - sometimes the effect is not immediate otherwise because of stored past data.