Thats still a lot of work to remove a tap. I dont know where u live but I would have removed it for you for $25 bucks and it would have only taken 15minutes. I work in a edm shop here in Michigan.
If that tap you broke isnt in bad shape hold onto it. grind it down flat......... Now you got yrself a bottom tap. Im reading a lot about people breaking taps on the forum. I would recommend getting a good machine tap. they are a lot sharper and less likely to break. also get some tap magic oil.