I re-built my program one shield at a time.
I discovered the errors started after importing the wire library - without even using it.
Some more research around "library conflicts" and I discovered I had most likely run out of SRAM!
As per the memory tutorial, I surrounded all my static (message) strings with F(), and all my problems vanished!
The UNO is a lovely device, but you have to remember its not a desktop PC with near-infinite resources....