I'm expecting to have the same issue with the Marceline's axe bass that I'm building, where the pointed tips on the bottom of the axe blade are bound to get banged up whenever she rests the bottom of the axe on the floor.
My solution is going to be to drive a long, thin, glue-coated metal dowel into the foam so that the end of the metal is just flush with the foam. With these reinforcements in place, when the axe sits on the ground, the part that touches the ground is the tip of the metal reinforcement rod, but the length of the rod (and the glue) distribute the weight to the foam. Like bones, I guess.
The metal dowels I'm using are the metal pegs that they used to stick election signs into the dirt - I scavenged a few after elections wrapped up :P