Imagine that you are "unit bar magnet" living on the surface of the floppy, and lying in the plane of the disk. One end of this magnet is North, and the other is South. To demagnetize you, we want to flip you completely back and forth, initially with some large amplitude, but gradually weakening with time. Your procedure with the permanent magnet did not achieve this result.

If you are absolutely determined to make a time-consuming/educational project out of this, you can build your own demagnetizer. The basic ingredients are an AC power source (isolated from the mains for safety), and an electromagnet. For the latter, you can wind your own, modify a transformer, or simply purchase one. You need enough ampere-turns to induce, say, a peak flux density of a kilogauss or so (easy enough) at the surface of the disk. Wave the thing over the surface, and gradually withdraw the magnet while continuing to do so. Once you get a couple of feet away, turn off the power to the electromagnet.

There's no need to repeat the procedure with the disk flipped over. The disk is so thin that the field will be about the same on both sides.