I've tried the alum solution on a high value 2024 aluminum part (don't ask). By the time it did anything to the tap, the whole part looked like acid etched sh*t. Yet there are many YouTube videos showing it working in real life. Maybe it requires old school HSS or more alum concentration or more heat. I dunno. My tap had a coating & maybe that slowed the whole process down. I tried carbide milling too but it was slow, tough sledding & pooched the end mill. Again maybe it was that particular tap. The spark erode machines are probably the weapon of choice but not for common mortals.
Stefan recently posted a video on a shop made micro trepanning carbide tool he ground. Something like that might be good, like a mini annular cutter. Core around the tap, pluck it out, fill the hole with native material / LT retainer, drill & tap again. Its not a fix for all kinds of parts but I have seen some remarkable saves where you wouldn't even know it was repaired.
Stefan recently posted a video on a shop made micro trepanning carbide tool he ground. Something like that might be good, like a mini annular cutter. Core around the tap, pluck it out, fill the hole with native material / LT retainer, drill & tap again. Its not a fix for all kinds of parts but I have seen some remarkable saves where you wouldn't even know it was repaired.
Pretty scientific, I know. 
It seems to me that it took about three days and the tap pretty much fell out of the hole. It was one of the last holes in a mini pallet I was making and only had time into the project, the alumm was an experiment to see if it worked. I believe the aluminum was 6061....