Fuel starvation problem.
 

Newbie here. First post.

Just bought a really nice '98 Mystique, 2.5L V6, Automatic, 25K miles. I have proven this issue twice. When the fuel level gets down to 1/4 tank or less and I get on the gas pretty hard starting off, it feels as if someone is switching the ignition off & on. Not a skip, a complete off/on. If I let up on the gas it smooths right out. It acts as if the gas is getting sloshed to the back of the tank and not being picked up in a steady stream. Anything over 1/4 tank and it will not do it.

Shouldn't be fuel filter, it doesn't care if the tank is 1/4, 1/2, or completely full as long as fuel is available. Shouldn't be fuel pump either, for the same reason. Shouldn't be rust, this is a fiber tank. My thought is obstruction of some kind in the tank, or in fact the symptom is exactly as it seems, that the gas is getting sloshed away from the fuel pump pickup.

Anyone else seen this?