So I likely need to ship my dog from Canada to Japan. I'm (I think) very well-informed about all the vaccinations, etc., that she has to go through (the process is maddening, as many things in Japan are

). I'm down to choice of air carriers, though. Was looking for some thoughts. My options are:
- direct YYZ-(NRT/HND) on AC, though for now, no seats available in J, so this may not be an option
- YYZ-ORD-NRT on either UA or NH
Any thoughts on the above? Has anyone flown with any of these airlines and brought dogs? Will it be a problem to transit through the USA? Will treatment be any different based on airline, or it's down to ground staff? My dog has never flown and is 10 years old, so while not a grandma, I want to reduce her stress level as much as I am able to.