Jumping Jack
Assuming you are talking about CENTCOM HQ at McDill AFB another option would have been to head over to the military ticket/travel office in the Exchange. No pain, no strain, discount tickets to the majority of the places worth visiting in Florida and beyond. I've done it a dozen times and seen customers with all sorts of allied uniforms in line.
When you are handing a valid prepaid ticket to the lads at Disney they don't care where you bought it (as it could be from any of a hundred discount programs), but buying it there can be problematic as you describe.