I had a 3/8" long piece of a Union Butterfield 1/4"x20 tap broke off in 1.3" blind hole close to 1" down in 6061 aluminum.I tried battery acid(sulfuric acid) for a week twice a day filling the hole with acid and heating till it bubbled with a propane torch,letting it sit for 12 hours ,flush with water and pick,managed to get a few bits of tap teeth out, but it wouldn't budge.
Then I tried the alum in boiling water for about 6 hours with no luck.
What worked was putting the part in a small aluminum pot of sulfuric acid on a hotplate set on
the lowest temperature setting outdoors.The battery acid is rather weak,but if you are careful,the concentration(strength) can
be increased by slowly boiling the water out of the acid and water mixture.I drilled a small hole through one side of the part to intersect with the blind hole so that the acid could circulate past the tap.It took about 2 hours and the tap was completely dissolved.
Be extremely careful with acid and the strong
fumes given off.Wear safety goggles,and have some fresh water nearby in case you spill acid on yourself.