I remember that if you had a ticket that routed on one of these "domestic-international" flights (on NH/JL at least) but you immigrated at NRT, you could still fly NRT-KIX. The airline would issue you a "domestic portion boarding pass" (国際区間搭乗票) that you'd show to immigration in lieu of a passport (since you still had to depart from the international section of the terminal). At check-in they'd write "CABO" on your boarding pass to denote that the airline was transporting you as cabotage (since NRT-KIX was technically an international route).
I did that too. Entered Japan in Tokyo, stayed a few days, then to Osaka for a few more days. I got a JL "international" NRT-KIX flight. I got that form, 3 copies (NRT immigration, KIX immigration, KIX Customs). Most of the people I had to deal with were completely confused about the whole thing. KIX Customs asked me where my arrivals card was when I handed them the 国際区間搭乗票 form.
