Call the clinic and ask if it is ok if you get the vaccines started and fax them proof to update your medical. You might get lucky and they haven't mailed it off yet.
The first two doses of Hep B need to be given 30 days apart, the 3rd dose is 6 months from the second dose. If you can fax all the vaccines proof that your GP gave, you might be able to have them mark off that it is completed. Without having to start over from square 1 in the US, as finding a doctor to just update and fill in the vaccine worksheet seems to be hard to find.