An apostille is, by definition, a chain of authentication, in order, from notary, up to and including the state department. It has to start at the bottom. Each step authenticates the previous step.

The final step is embassy authentication, if required.

Depending on which state you are in, the hardest part might be getting a notary to stamp your logbook. If they won't, you might try writing an affidavit swearing the authenticity, sign in front of a notary, and have them notarize the affidavit.