So this is the pill box concept I was referring to:
https://www.thingiverse.com/thing:4936862/files
Pictured here is the half version
If you look through that Thingiverse page you'll see a full 7-hex version and there's ones with door openings. I was thinking a few of these could be stacked to the appropriate height making sure to have a good opening at the top and bottom. The dice would empty out on to your map, maybe some water tiles or something and use castle battlements for the backstop. Then you'd build the rest of your map around the central feature.
Example (pretend the stacked 7-hexers are the 3d printed hollowed out ones)
