I happened to transit HND three weeks ago as well, although straight through on JAL but the process is the same. Pick up the luggage, and once you get into the arrival hall, turn right, walk to the end, and you'll find the counters to drop your luggage. It's a fully manned counter so you can do pretty much everything you need here as well, e.g. if you didn't get your onwards boarding pass, you can pick them up here. The domestic screening checkpoint behind the counters opens at 6am IIRC, but there would still be a bit of a wait for the first bus so if you have an early flight out, say, departing before 7:15am, you would want to head for the bus outside. Otherwise, the domestic transfer bus will drop you off airside in the next terminal. Note that ANA has quite a few more buses, but each airline can only take their own passengers as they operate from different terminals.
Not sure if the JAL class J is really worth it. It's a slightly bigger seat (if you are on a 738, it might be in a 2-3 config). The points and status earns on dom class J have also been enhanced post simple-and-fair so it's a bit like throwing money away for a slightly bigger seat for a flight that's not much more than half the distance between SYD and BNE.