Organic potting mix...probably has a bit of manure(nitrogen) of some sort in it. Do you also fertilize? Do you thin them early to an inch apart? How well do the greens make...nice and green? I wonder if you were to add some sand to the potting mix if the structure would be more favorable for radish?
Planting deeply, from what I understand, can prevent the radish roots from "popping out" or whatever...pushing the top of the root out of the ground. I read somewhere that an experiment with planting an inch deep and an inch-and-a-half deep. Seems this prevented popping out but also the radishes performed better than others that were planted at the 1/2" recommended planting depth.