Originally Posted by Hans
I am guessing it is a crack or hole around the filter.........that occurs only when the pump is on.
I agree. The leak must be such that it sprays downward onto the road when you are driving. Even so, it is hard to imagine that you don't see a splatter pattern under the car behind the filter with such a rapid rate of loss. Do you see this? Is the new filter wet? Have you tried running it in the driveway and watching closely? Put it up on stands or on ramps? The oil pressure relief valve should open at about 60 psi. Maybe your relief valve is periodically sticking closed and allowing intermittent high pressure to build which then blows oil out through a small crack, or past a gasket that is OK under normal pressure.
[edit: Don mentioned the sending unit. They can come unsealed and leak under high pressure, too. All this stuff is in the vicinity of the oil filter, so it seems some careful observation ought to pinpoint the problem.]