If I understand you correctly, wouldn't it be easier to start with a coping saw blade?

Tell you what I have done with broken bolts that just would not come out . Take a hacksaw blade grind the back away about one inch long grind it to the width of the hole you have drilled . Put the hacksaw in the hole saw through the bolt once you have a cut in the bolt it will collapse in the hole and come out . Sounds crazy but it works for me

I had good luck extracting a broken bolt with a Rescue Bit (rescuebit.com). I was able to remove the broken bolt, and the threads were still intact. I was able to replace the broken bolt with the same size bolt & thread pitch. The bits aren't cheap; however, being double-ended, they have a longer lifespan. You might want to try it before removing the head and taking it to a machine shop. Be sure to follow directions, and let the bit do the work. 

Drill it larger and larger to get enough area for an "easy out".  If you need to remove the threads, then re-tap it for a heli-coil.  Should be something you can do at home if you have the room to get at it with a hand drill.  Joe-JDC

JDC

This bolt broke off in my head while taking the manifolds off. Tried cooking for days in deep creep, tried heat, welding a nut on it, drilling, etc. It just keeps destroying my tools. 😩

If I'm taking them off and over to a machine shop, what else should I have them do?
Looking for advice and suggestions.

1964 Ford F100 w/ 292 Y-block
-Central Florida-