David

There are several options.

Grind it out with a Dremel tool and grinding tip.

Drill from the other side and beat the tap out with a punch.

Break up the tap with a punch. Fish out the pieces.

Do as you did and drill a larger hole next to it and break out the tap.
Then drill a yet bigger hole and fill it with a stud. Grind smooth.
Drill and tap again.

Bob AZ