Individual countries and airlines determine their own regulations about access for assistance dog teams, and as you know, some only allow access for teams that were trained and certified by an Accredited ADI Member or International Guide Dog Federation (IGDF) program.
ADI does not make these determinations or have any influence over decisions about access for individual teams. You may need to work with the disability services department of the airline to see if there are exceptions to the regulations for access both in the airport and on board the plane.
ADI or any of our member programs do not just administer tests to verify or certify any type of assistance dog. The only way someone who has personally trained their dog may receive verification from an ADI accredited program would be to become a client of an accredited program. Some ADI accredited programs will accept a privately trained team for evaluation and possible further training/certification, however ADI standards require that there is a minimum six-month training period for these teams. There are no exceptions to this standard.
Guide Dogs UK has developed a web page that has specific information about international travel for Guide Dog/Assistance Dog teams. This may also be helpful to you.
Another resource you may wish to contact is the International Association of Assistance Dog Partners. This is a worldwide consumer group of individuals who have assistance dogs. They have travel information on their website and members you can contact about to ask about travel issues, etc.