One very simple thing you want to inspect for.....
Remove the oval air filter tube from the front plastic shroud area and inspect the hole it attaches in to. That hole should be free and clear of black plastic. The shroud itself has a plastic flap that if the shroud was removed and flap not position properly when being re-installed, there is a serious air flow obstruction.
I don't recall what year it was, but some time after 2007, Ford had a recall on this very thing. During that model year for a number of months, someone on the Ford assembly line was mounting the black front shroud with the flap not folded back properly, causing that air intake obstruction. Every E-series was recalled and inspected to make sure the flap was folded back during assembly.
With our 2007 E350, we ended up with a large bird plastered on our radiator. I removed the shroud trying to gain better access and sure enough, I had to be mindful of that flap.
I imagine the obstruction would affect high-demand acceleration.