Yes, the force between the magnet and the cooper pipe is proportional to the relative speed, so you can leave the magnet still and move the pipe and get a force that cancels the gravity.
But in a real experiment, I think that it will be very difficult to keep the magnet in the right position, it will rotate and bounce against the walls, and the force will vary, so the average force has to be equal to the gravity. So your experiment is ideally possible, but I think that it will be very difficult to implement.
(In the original experiment, after a few moments, the magnet falls at an almost constant speed. This is the same speed that the pipe should have in alternative experiment.)
But in a real experiment, I think that it will be very difficult to keep the magnet in the right position, it will rotate and bounce against the walls, and the force will vary, so the average force has to be equal to the gravity. So your experiment is ideally possible, but I think that it will be very difficult to implement.
(In the original experiment, after a few moments, the magnet falls at an almost constant speed. This is the same speed that the pipe should have in alternative experiment.)