Dominic,

Great question. Z-Score was designed mainly for use with manufacturing companies so to apply it to banks naturally would require much tweaking. There's some published research on the subject using a bankling sample (such as paperhttp://www.sciencedirect.com/science/article/pii/S104244311300005X).
Alternatively, SRISK, a measure that Prof. Robert Engle developed to estimate how undercapitalized a financial institution can become in times of crisis, may also be useful. See my interviews with him for more details.

https://blogs.stage.cfainstitute.org/investor/2014/07/16/nobel-laureate…

https://www.cfainstitute.org/learning/products/multimedia/Pages/127225…

Warm regards,
Larry