I did LAX-HND-KOJ on NH earlier this year and while the process is not as smooth as other airports (ie terminal change that railroadtycoon mentioned), it's really not that bad. You go through immigration and customs and after you exit customs, there are transfer counters to the right. They'll take your bag right there and in your case, you won't see it until you get to ITM. After that, onto the shuttle bus between terminals and once you're at whichever terminal you need to be at, you go through the security and voila, you're airside.

I agree it's not as convenient as flying into KIX directly from the States but it really isn't a huge deal. Three hours is plenty of time.