You can fake an EDM in a temporary way with an aquarium pump, distilled water, a plastic pan, a 12v battery charger, and a very steady hand. The bigger the charger, the better. You are only eroding the centre web of the tap.
It is more tedious than TIG welding, but you can erode away the tap with an arrangement like this. I did this only once, about 30 years ago. It took 5+ hours for a 1/4 tap, but it saved the part. I can't remember how I grounded it, but the current CANNOT pass between the tap and the aluminum hole or you're sunk. I think I used a copper wire to touch off on the tap. The electrode can be anything, but I used a piece of copper coated steel welding rod intended for oxy-acetylene.