I did a some checking for you:

At the moment, little to no F award on any JAL flights on either LAX-NRT or ORD-NRT from March - end of May. I did, however, see decent availability for business class awards.

There are, however, plenty of AA F on LAX-NRT, and plenty of JL F on NRT-CGK. For example, here is a search for the first two weeks of March, traveling LAX-NRT on AA F and NRT-CGK on JL F: Award Nexus Search Result

It doesn't look like there are 3-class F on the NRT-CGK scheduled from April onward, at this point.

The NRT-CGK JL flight departs before noon, so essentially there will be a forced overnight in NRT, as most if not all US arrivals arrive after the CGK flight departs.

You have a few options. If you find AA First acceptable, book on AA first (with options that include some non-stop on DFW-NRT in F), then switch to JAL if and when that becomes available. Alternatively, you can book on JAL Business now, and seek to upgrade to First, if and when that becomes available. Either way, there should be no fee to make the change.

Note that JAL has just announced updates to 773 cabin products. New first and business class (with direct aisle) are coming online in 2013.