One way of tackling this problem would be to use a smart combination of selection criteria – for instance, combining a balance sheet threshold with a prudential decision based on the institutions' risk profiles. But there are still many crucial details and potential pitfalls that need to be addressed before we can even begin devoting serious thought to an option of this kind.
This is something I think we should consider with an open mind. A systematic approach, assuming it's feasible, is usually superior to an approach based on workarounds and emergency repairs.