You need the police clearances. The 10 year period has to do with qualifications, not police records. You should contact them and tell them you're in the process of obtaining them. Hopefully that will be ok.
You don't need to request fingerprint cards from the U.S. The FBI website has a downloadable fingerprint card for you to use.
http://www.fbi.gov/hq/cjisd/fprequest.htmJust print it out and get the fingerprints done in Japan. To expedite the FBI check, you should
1) send it to the FBI via courier and write "please expedite" on the outside of the envelope - include your 'due by' date
2) write "please expedite" on the request letter itself, and include your 'due by' date
3) enclose a pre-paid courier envelope of some sort.
The FBI won't accept a credit card number to bill return shipping, so you have to provide the postage either in stamps or by using an account number. When I did this, I had to obtain a FedEx account number for myself. The FBI then FedEx'd my police record back.
Police certificates are only valid for 6 months. So yours have expired.