All that needs to done is devise a way to whitelist customers, without it becoming too much hassle because that is Bitpiggy's strength, that is easy and simple to do.
What I would do first is whitelist all customers that have used the Bitpiggy service and open backup.
Next I would get bank accounts at all four major banks and suggest people transfer money to the same bank as their own, then maybe same day transfer of btc could be possible instead of 24 hour wait. (overcoming a shortcoming of bitpiggy)
Next is growing the whitelist of good customers, maybe simple things like allowing them to buy 1 btc, then they must wait a week and after that if there is no fruad problem move them to the whitelist. Sure they could still scam a single btc but they risk losing a bank account they have access to for $5.
Goodluck with whatever you do. I have only had very good experiences with Bitpiggy and look forward to them returning.