that sucks dude, we have all been there and done this.
here's what i do, and what you might try in the future for any kinda stuff like this.
I broke a bolt off in a brand new nos sachs head and it was way down inside and way beyond my ability to get it out. I tried a whole ton of machinists and they wanted to do an expensive excavation, heliarch it , and retap it for 100 -150 dolllars. no way.
So i thought "who breaks studs all day and is good at fixing them" and went down to the local european motorcycle shop and asked to speak to the mechanic. I said "hey i did something reallly dumb but i bet you know how to fix this. This is only worth 50 buck and everybody wants to charge me more then its worth to fix it, what can YOU do? I cant spend more then 30 bucks on it."
he said he's take a look at it and call me...
After lunch he called me and left a messagae saying my "little head" was ready for 20 bucks and to come get it.
he re drilled and tapped it right, and gave me allen screws so it wouldnt happen again.