Why does my calzone crust lose its crunchiness within minutes of being removed from the oven?
The lack of vent holes would have been a problem.

Vent holes allow steam to escape, reducing the amount of internal moisture.  This moisture will both prevent the crust from cooking fully through, and will cause the crust to soften as after it comes out of the oven.

That's not to say that there wasn't also some other problem, just this is one thing that you should correct.