I was stationed in Yokuska myself in 1995... I put my car in storage for a month until my Dad could retrieve it and take it to NY (from WA). I could buy gas on the base at near US prices, but Japanese fuel is one step above kerosene... and about a $1 per liter in town. Will have a hard time manuevering it in town for sure, due to its size. I would check with your financing company as well, they might not allow you to move the vehicle out of the country. You will have to buy Japanese liability insurance, and obtain a Japanese drivers license, so the $3000-$5000 is about right. I ended up buying a used Japanese sedan from a family PCSing back to the states. Was only $800 for the insurance, since the car was already registered with Japanese plates. Remember too that they drive on the Left side of the road, a further disadvantage...
I would find a way to store it, especially if your hitch is only a year or two. That way you will have reliable transportation as soon as you return to the states. Used cars are easily obtainable and cheap in Japan - the Japanese seem to throw their cars out after the first scratch, and once a Gaijin has owned an auto or rented a house, no Japanese wants to drive or live in it... Lots of turn over on base, the 4 door Camry we bought was only $1700, and was 4 years old, perfect condition.
Good Luck, if you haven't been before, you have a great adventure awaiting you - get out and explore as much of Japan as you can!