I have a story someone told me many years ago in a bar. Take it for what it's worth.
Said guy was relating a story about a car he had. It would intermittently die on the road. It would only die while driving. After sitting for a few moments the car would start back up and run fine for awhile. Maybe 10-20 minutes, maybe hours or days. This was back in the 70's or 80's, so before electric fuel pumps were common.
After several visits with the dealer they finally decided to inspect the gas tank. Lo and behold when they emptied the tank a plastic sandwich bag came out. I don't recall, but this may have only been an issue when the gas was below a certain level, as in the bag had a tendency to float and only got caught below a half tank.
Seems it would float around until randomly covering the pickup screen, when the engine died and the pump was no longer creating suction at the pickup the bag would float off until the next random event.
I don't how much trouble it is to drain your tank for a detailed inspection but at least you can rule out any scenario similar to above. I don't think dropping the tank but if you could get it empty and inspection with a bore scope may prove helpful.
I would not recommend going through this trouble until you've exhausted the more common problems and remediation.
Kevin