I`ll give "friendly" advice.
Have an emissions test done in the US, and have that translated to Japanese. It will allow you to run the engine once in Japan - otherwise no further tests can be done. I`ve never personally imported a car - however, a friend of the family brought a car in from Europe. That snagged them, and it ended up taking 3 months before they had the car in hand. Also, be sure to bring along all the documentation you have for the engine.
Updated motor, new parts, etc are all great - but there is still a fairly high probability you`ll have to have things modified quite a bit before passing the Japanese tests. Emissions are only a small part. There are limits on the exact directions for lights, the color range, materials used in the interior, etc etc - it will probably be the small things that will take the time for you.
The average cost for checks, modification, and registration is about 1,500,000yen for an individual. If they deem the new engine unsuitable, or the body out of limits, it may leap to many times that.
Anyway, out of the gate you`re going to have to have transportation set up to move the car to a private lot - you can probably contact an international dealership to take care of the rest for you.
(And everyone beat me to it.
Here I was flipping through a 個人輸入 book...)