ISpeakForTheSeas said:
The only things that I've read about which confirmedly prey on Vermetid snails are
Carpilius convexus (a crab),
Mancinella armigera (a muricid - A.K.A. murex snail), and
Menathais tuberosa (another muricid snail). For hopefully obvious reasons, none of these are fully reef safe, as there's a very good chance they'll eat CUC and any bivalves you may have (and with the crab, pretty much any other invert they can reach may be in danger as well). It's presumed in the report I've read that other
Carpilius spp. will eat them as well, and there are likely a number of other muricid snails that would eat them too. I have no idea if these would be coral safe or not though.
So, while they're not common in the hobby, you might be able to get some Carpilius crabs, or you could try getting some predatory snails and see if those help. Some of the smaller predatory snails may be able to reach places where fish would struggle to, but there's no guarantees. I've heard some people have luck with bumblebee snails, some with emerald crabs, and some with wrasse or butterflyfish (possibly pufferfish too) - those might work, but from what I've heard it's very hit and miss - as you've seen (it may depend on the species of vermetid). To my knowledge, though, none of the likely to succeed possible predators are totally reef safe. Either way, biological controls may help to limit the population, but I wouldn't expect a complete eradication.