We sometimes have accounts giong dormant where the branch people know the customer and we make contact with them that way. For the others where mail is not getting to the customer I think you have done all that is required and is cost effective. Since the money doesn't just dissapear, the customer can still get it from the state.
Some states even host a web site sponsored by the state controller, treasurer, etc. where people can put in their name and find out if they have funds that have been escheated to the state and they can then claim the money.
My opinions are not legal advice and are worth what you paid for them.