A-ha, you didn't say you had a wood floor! That makes a big difference, since the two examples I gave you rely on the thermal mass of a stone or tile floor. Wood is more of a thermal insulator, which in the case of a floor will slow the rate at which the heat source below it loses heat to the living space above. This could be a good feature, as a high thermal mass, like you are thinking of, will keep the room above warm for a long time.
But in your search for a good thermal mass, don't limit yourself to dirt. In this
table of specific heats, you can see that water has 5 times the heat holding capacity of granite. Maybe the best thing to do, since this is not your own place, is to use your rocket stove to heat a big tank of water in the crawl space. Then when you move, you take your tank with you.