Thank you for the reply! This is helpful. I'm sad that for all the details I've provided, I forgot to actually say WHAT kind of dog it is (to illustrate cabin (non-)eligibility)

It's a Shiba Inu, so being a shade over 20 lbs, she's definitely not going in the cabin.
Noted regarding UA, so that option is out. As for transiting YVR - I was considering that, but the staff wouldn't walk her, right? And I don't think I would have access to her when in transit, would I? I don't imagine she'd make it for 14 hours (she can do that at home, but the stress in the plane is likely to make her 'go' - I was going in with the expectation that things will go off the rails and I will get a stinky dog that'll need a bath in Tokyo). Or are you suggesting I make an actual stop in Vancouver, so I can get out of the airport and overnight there or something?
Shibas are extremely clean, and *never* do their business 'in their home', so subjecting her to flying in her own poop is likely to cause undue stress. So I suppose ideally, if there's a possibility to get access to my dog in YVR, I would definitely prefer that.