Major holidays are difficult, but otherwise both ANA and JAL have very good availability up to the last minute,.
With BA miles I can often book JAL domestic flights with Avios as late as three days before the flight departs. For example, looking at the BA site today (18/May), I see JAL domestic award flights for Sunday (21/May) but not for anything before that.
Using JAL miles, I've been able to book JAL domestic awards when they're no longer available on the BA site. I might be mistaken but I think the number of miles required was higher for a last minute reservation. (Or perhaps it was just that I was flying on a peak travel date).