The added shielding (tin can method) is the way to go IMO.
The aluminum foil didn't work because aluminum is not ferromagnetic. (Foil's too thin anyway.) The only "common" ferromagnetic materials are iron/steel, nickel, and cobalt. The only really practical choice is steel.
I'm a little surprised that so much magnetic field gets out of your steel case. Does a magnet stick to the side of the case?
If you picture the way magnetic field lines loop out from the North to the South pole of a magnet, you can picture what the shield is doing. It is "easier" for a lot of the magnetic field lines to take a shortcut through a piece of steel (where they can be closer together) than to loop out through the air. A tin can surrounding the pump gives the magnetic field lines a shortcut to get back to the pump, and they don't reach out so far. A given amount of steel can only hold so many lines though so the thickness may need to be increased to get adequate shielding.
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