This would move the magnet down about 2 mm. Shouldn't affect how the unit works at all.
Since the sensors on the PCB below the magnet measure the strength of the magnetic field, I think moving the magnet 2mm would have quite a profound effect. I'm pretty sure you can't move, drill, or otherwise modify the magnet in any way.
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What
would work, is to give up on the idea of wires altogether, just as Wico, Happ, and other top-fire arcade sticks have done. You need a plunger in that hollow shaft instead. Now, in other topfires, the plunger just pokes out the bottom and hits a switch; not an option here, due to that pesky magnet again.
So what you need is a plunger that stops just above the magnet when it's pushed all the way down, and rests a few mm above when it's not being pushed. Two vertical slots are cut in the bottom of the shaft, 180 degrees apart. The slots are the same length as the plunger's travel distance. Attach a cross-member to the bottom of the plunger, that protrudes out of the slots. A pair of disc-shaped contacts are attached to the shaft between the magnet and the cross-member. These discs must be mounted so that they can rotate freely around the shaft, and have a soft spring holding them apart. Wires soldered to the discs can be tied off to the frame of the joystick assembly, with enough slack to allow free movement of the handle and a suitable strain relief to prevent damage due to constant flexing.
I can see it in my head, but I'm not up to the illustration right now. Hopefully my explanation is clear enough.