I just called all over Japan and the cheapest price I can get is 75,000Yen, which at the current yen rate is about $689. I called the base terminal and they only accept pets from people who are PCS'ing (moving for good). There is a ton of stuff to get worked out for this to happen... but it just might work.
Since the last thread the policies have changed and you can no longer bring a pet onboard an aircraft. They have to travel via a shippign service. The quote that I have is for a place called Yamaguchi who can get Boomer shipped directly to Dayton.