What you could do is make a copy of the last (or more) page(s) of your logbook, place a text somewhere like "I, .........., hereby certify that this is a true and correct copy of the last page of my Pilot Logbook, used to record flight experience in compliance with the requirements of the Federal Aviation Administration", and then go to a public notary and sign it. After that you can take that piece of paper to a local office of authentication services and have it apostilled for the country you want to use it. In DC it is like $ 15 per page, the link to the place in DC is:
Notary and Authentication Services | os