Not accelerating properly

Your description of the symptoms matches what happened to twice my '88 Grand Caravan. It had a very elusive solution the first time. Suspect the fuel strainer in the fuel tank is plugged or collapsing. This occurs after many miles during that drive cycle, then begins to occur more frequently over the next few months. This photo shows what it looks like. It's snapped onto the bottom of the housing the fuel pump sits in. One of the clues is the engine runs okay after sitting for a few minutes.

You can verify this by connecting a fuel pressure gauge and running the hose under the rear edge of the hood. Clip the gauge under a wiper arm so you can watch what happens to fuel pressure when the stalling occurs. There's usually no test port on the throttle body assembly. You'll need to fashion a tee to connect to the fuel supply hose.

Normal fuel pressure is 14 psi. You'll see that drop gradually if the strainer is plugged, then the engine will stall once that pressure drops low enough. This problem is not affected by the level of gas in the tank.

An even less-common cause is a dry-rotted fuel supply hose in the fuel pump housing in the tank. That's shown in the second drawing. This one is affected by fuel level. Air can be drawn in through the hose once fuel level gets down to that point. Unlike with the strainer, the engine will not run okay after sitting for a few minutes. The best clue here is the fuel pressure will drop off very quickly once the engine is stopped. Normally it should hold for days or weeks. The leak is inside the tank, so you won't see or smell any gas leaking outside.

Also check out this article on fuel pressure testing:

https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator