A little while ago I stumbled on EBay suppliers selling DS3231 modules for around £1.50 each for a complete module so I purchased a couple to experiment with and see how easy they are to use.
Today I upgraded my clock to use that module. A little bit of fiddling with the original PCB is required but it can adapted relatively easily. A few changes were also required to the clocks original firmware.
Anyway it's been running on the bench for a couple of hours without any problem, so I'll publish upgrade details soon. I'm also going to re-publish an updated version of the original design.