I'll pop this as a top level comment, as so many people have made recommendations, thank you everyone!
Valetudo absolutely sounds like the way forward.

After more digging, it looks like mopping, unless you spend lots of money, is kinda basic on all models.
So I've gone with a basic second hand machine that works with Valetudo, and has simple mopping.
Hopefully it'll let me get a good idea of what is/isn't possible, and if a £600 full on mopping device is worth it!
And who knows, if spending that much is worth it, I can have one on each floor, like a fancy rich person.

(I also need to find out how well machines deal with poo!)