Nice idea. It would pair with the ability to hot replace buildings lower in a stack without destroying and rebuilding a stack. Consider: putting a stairway through wooden platforms, but the 3x height platform is not at the right height.

I had a similar idea as well. Mine sort of expands upon the OP's in that it would allow the beavers to excavate dirt by hand without needing to build a dirt extractor. The production of dirt would of course be slow and time consuming but it could allow tunneling and other dirt based constructs earlier in the game. Think about having an earthen dam instead of a log dam or building elevated agricultural areas earlier.

I also was thinking of adding a whole dirt excavation tree. Think shovels, excavators, bulldozers, strip mine (aka dirt extractor). This would probably be an Iron Teeth thing but maybe something could be adapted for the other factions as well.