I may be able to offer some assistance with this one. The US Military postal system has changed at least once since this stamp was canceled. While I am not familiar with the current system (at least not as much as I would like to be) the postmark you have is most likely for a military base in the Republic of Panama. Here is another cover with a similar postmark from my own collection.

It is interesting to note that this cover was sent from a US Army Base (Fort Davis), it is postmarked by the US Air Force Postal System. This is because the bulk mail sorting was handled by the US Air Force. I know that the various US military postal system used a few different zip codes based on 340xx. I believe that 34001 was the zip code for the Albrook Air Force Station.
It is interesting to note that the bulk of mail sent from the US Military Postal service in Panama was sent from the Albrook AFS postal station as all US Citizen civilian employees for the Panama Canal were assigned that postal station (as a continuation of the Canal Zone Postal Service which ended in 1979).
That's my epic book for today.