Cubby-holes lose something along the way though. I have faint memory of visiting a relative whose grave is a marker on a wall- likely a soldier- and it comes up very lacking compared to a headstone in a field.
How about this: When a cemetery is "full", temporarily remove all the headstones, add 10 feet of dirt over the whole site, then replace all the headstones in the original positions. Now you can start burying more people. What's wrong with that? People are still buried, you don't have to dig people up, what difference does it make if people are 6 feet under or 16 feet or 26 feet.
San Diego did almost exactly this. There is an old cemetery there where they removed all the headstones and buried them in a mass grave, but left the bodies. Then they put a city park over the bodies and children play there now. I'm serious.
That's how Cheeseman Park in Denver was created, too
That misses the problem. Where do you put the new headstones?