Hi Carrotcake. We just re-did 3 bathrooms in the house and got the heated mats in all three. I have to say that I was a bit sceptical about getting them but hubby is in the business and so we went ahead with the mats. I have to say, that they are terrific. They really make a difference - our downstairs loo didn't have a rad in it and the mat really takes the chill of of it (room was always really cool).
As regards changing the tiles, the mat would have to be replaced - but not the probe or the control panel. therefore you would just replace the mat which is not too expensive.
I thoroughly recommend them - only have them about 6 weeks and I'm really thrilled with them. If you've any more questions let me know.