Can confirm after an hour waiting on hold for a VS agent this morning (much easier with Pixel "Hold For Me" feature) a VS agent ticketed the flights I wanted in 5 minutes. I also see the single seat I found no longer available on united.com, so I believe that shows that website is pretty accurate at inventory!

This will be my fourth attempt to go to Tokyo, so fingers crossed.

EDIT: Also obviously a British agent (Even through US number) and the total was around $200 in taxes and fees .. so less than the $250 I paid a few years ago, but much more than the $50 I paid last year. But of course at this point I just want it to happen!