Looking short-term (next few weeks), it seems like there's a lot of BR J availability on North American routes. Further out, de nada.
As the blog linked above suggests, looks like BR is trickling stuff out starting three months out, and opening the faucets at three or four weeks out, turning into a deluge within a week of departure.
(5 J seats available on BR35 on Wednesday, in case you have a last-minute hankering to take the whole family to Taipei.)