A Little More Background on Batillaria
I did some extensive searches and was unable to find any studies published on Batillaria minima. There has been some phylogenic research done on members of the Batillaria genus in Japan, but this article did not address how B. minima fit into the phylogeny (Kojima, et al. 2001), though they did decide that there is considerable work left to revise the distinctions among species in the Batillaria genus. .
There was also an interesting study done on B. comungi that found populations living on mud substrata were on average longer in shell length than those living in the rocky intertidal (20 mm compared to 15 mm) (Adachi and Wada 1999). This is interesting because Batillaria minima is typically found in mud habitats, though I encountered them and did my research on them in a rocky habitat. I also found, when I was trying to identify my little snails, that the shells I had collected were not quite as long as the 15 mm shell length given in Wolfgang Sterrer's description, making their identification a slightly more challenging task. Food seems to be more readily available for these snails in mud, and I would agree there appeared to be very little food of any kind (other than Batillaria and a few hermit crabs).