Don't gloss over the size difference in the 3 bolt setup and the 6 bolt setup. They get bigger when they use 3 for a reason. Just sayin...
And also notice that the holes will not line up as you go from a design with three to five, or from 5 to 6 bolts. There's a reason for that. Someone with an engineering background must have thought that it's best to spread the forces evenly or something.
I know one that wanted us to put small pieces if 30# paper on either side of a 2x2 that was sandwiched between two rails, because the 2x2's were only 1-7/16". Yeah, no.
Man dont pay to have that fixed, do it yourself. Its super easy. You could... 1. Drill at tap for a larger bolt 2. Drill and helicoil for original sized bolt. Either way takes 5 - 20 minutes depending on how much experience you have with the tools. If really unsure get a scrap part from a junkyard and practice on it first. You'll still be money ahead and have a safe part.
To get back to the OP, you can try dissolving the old bolt with alum. Several tutorials on the web for it and it will preserve the threads, so no drilling, tapping, or helicoil.
I want to have a machinist do the work since I suck at this type of stuff. Any recommendation on a shop by nyc?
Watch some YouTube videos then go slooooooooooowwwwww. It's super easy and puts another skillset in your toolbag that you'll always have at your disposal. Trust me....super easy.
If the bolt is broken because the threads are crossed, then you need a machinist to make sure that the new threads are perpendicular to the mounting surface. If the bolt is broken because someone gorilla tightened it, then you can likely just start drilling it out and could simply thread itself out the backside of the rim. Just start with a 1/8" drill bit, then a 5/32, then a 3/16", stepping up to a 1/4" bit. By the time that you get to 1/4" (or before), the bit might catch on the previous hole size and just wind it down into the center of the wheel. Or, by that time, you would have it the right size to use an easy-out. It really is that easy. Just use new bits, some type of lube (penetrating oil of your choice), low speed, and constant pressure straight at it. You can do this!
I am on the other end of the state otherwise I would help you out. There has to be someone semi local and skilled that can help you learn some new things and fix your wheel up.
Is the bolt one where it has a shoulder that sits down into the carrier a bit? You're going to want that bolt pretty well centered if that's the case or your going to have issues later.
I'd drill a larger sized pilot hole (a few sizes smaller than bolt size) and try to extract with a tool after hitting the area with lots of mapp gas... maybe dremel the top before drilling... maybe