I think a limited amount of chests located in the bank (like safety deposits) is the way to go, because the current way (the block on top) doesn't work, people don't care, they just destroy the block and then take the stuff inside. I think the bank should have a chest (or 2) for each person, where they can put valuable stuff.
Another idea is you might be able to build/make a plug-in where there is one chest in the bank, and then depending on who opens it, it has their safety deposit inventory, then when they are done, they close it, but to the next person it will show their inventory not the first persons.
Post ideas and comments below