[1] For these two senses of the headword (here in the accusative case and glossed as in Homeric scholia) see again theta 387. The basic meaning seems to be "pile of sand," usually on the shore. According to Chantraine s.v., the word appears to be attested in Mycenaean but has no known etymology.
[2] Aristophanes, Wasps 696-697 (web address 1); 'depth' uses the headword figuratively. Indeed, a related sense of the headword is of sand or mud on the bottom of the sea; cf. LSJ s.v. qi/s A.3 (web address 2). Thus, to develop the metaphor, perhaps: "you disturb the utter depth of my soul".
[3] Greek Anthology 6.62.3-4 (Philip of Thessalonica); cf. kappa 1670. On this epigram, the scribe Callimenes's dedication of his writing instruments to the Muses, see Gow and Page (vol. I, 304-305), (vol. II, 337-338), and further extracts from this epigram at kappa 316 and sigma 742. Gow and Page suggest (vol. II, 338) that Callimenes used the pumice to refine the nibs on his pens, already roughly shaped using his chisel (smi/lh; cf. sigma 742).