I'm not saying you should or shouldn't go to Europe, if you choose to have surgery, but I'm not sure it would make sense to travel abroad from a cost perspective. Obviously, this all depends on what your insurance will cover, if anything. I would start there.
Does your plan exclude orthognathic surgery? If it's included in your plan, do you meet the necessary requirements? (Requirements vary by plan, but you often need to meet specific measurements and potentially have functional issues, too.) Even though you have a high-deductible health plan (HDHP), I think the maximum your deductible can be is something like $6,350 (individual), and $12,700 (family). Unfortunately, that will not get you far traveling elsewhere. Prices may potentially be less elsewhere, but when you factor in the cost of braces, surgery, and travel (this will obviously be a lot); I just don't see how that's cost effective. Not to mention, if something goes wrong, it's both expensive and a pain in the ass, to find a flight to Europe in a pinch.
Good luck with everything!