The 707 E-6B (E-6A as delivered) has a history of tail "issues" going back to initial flight testing on aircaft TO251, the prototype. Structural flutter was discovered while trying to demonstrate contractual dash speeds. On the first attempt thought to be low enough risk to not warrant a chase plane or dedicated instrumentation of the vertical stabilizer, about 40% of the vertical stab and rudder departed the aircraft over south Puget Sound. The flight crew knew something had happened but had no idea of the extent until notified by the tower on short final to Boeing Field.
Unable to determine the exact cause our crew spent months restoring the aircraft, instrumenting everything in the tail section, and going back out to repeat the flight profile. This time with a chase aircraft over the Olympic mountains Result:

Same as before. Actually a bit worse as the instrumentation wire bundle inside the vertical stab held the parts together long enough to swing them over and take out several feet of the horizontal stabilizer and elevator. The stabilizer attach fittings were a mess as having already been repaired, leaving the machine shop artisans at Boeing with an impressive task to repair the second time, truly hand built.
The ship was restored again, a fix determined (thicker outer wing skin panels, lower dash speeds) the flutter profile flown a third time (less one of the original pilots) and passed.
TO251 finally delivered to the Navy. Squadron VQ-3, located at Barbers Point Hawaii at the time received this aircraft in a special ceremony and christened it with call sign "Gecko One" and installed a tail-less gecko stencil on the nose gear doors.
Going back to the hangar door cut-outs - the 707 vertical stabilizers had a laydown tool that allowed the tail to lay over horizontally when entering hangars that lacked doors tall enough to accommodate the new aircraft. The Navy used the tool in Barbers Point and at Pax River for the sister squadron VQ-4.