Herb,
If you’ve really given-up, you’ve received plenty advice on how to find a machine shop. But, if you want to try again, here’s what I’d suggest:
1. If the extractor broke-off flush with the bolt (ie., there is nothing left to grab), I would use a thin penetrating oil (like Liquid Wrench) between the extractor and the bolt (to remove the extractor). Once the oil had time to penetrate, I’d take a Dremel tool and cut a slot in the extractor (screw driver slot). Then I’d take a manual impact wrench (hand hammered) and try to back-out the extractor by putting a straight blade in the slot you cut. If the extractor is too deep that you cannot cut a slot, I’d use a punch and hammer to reverse thread/tap-out the extractor. Note: extractors are reverse threaded, so you will need to reverse the reverse direction to back it out).
2. If you successfully remove the extractor, you have four options (and combinations thereof) to remove the bolt: (a) brute force with another, larger extractor, (b) drill-out the bolt, (c) use a solvent on the thread sealer which secures the bolt, or (d) heat the joint to melt the sealant and provide a hot/cold differential between the bolt and the holding piece. Blue Loctite should not need solvent or heat, so I suspect the breakage of the extractor indicated the bolt was locked with Red Loctite or similar factory sealant. I believe Red Loctite and the factory thread sealer are temperature sensitive and can be softened with heat. I haven’t used the plumbing product Sailariel suggested, but if it eats plastic, it may soften the thread sealant. I wish you luck. Note: some permanent thread sealants are designed to withstand high temperatures.