Beware that UFH can KILL pianos!
Oh, how so? We have UFH but no piano as yet.
Electric mat UFH is very easy to fit and doesn't take up any height. In the cottage in Wales it's been a revelation compared with the previous early-morning frigid tiles laid more or less straight onto bare mountainside [1]. We inherited it in the bathroom of our previous concrete second floor 60s flat, and put in wet UFH everywhere else. Unlike the main system we never really optimised how to use it: the thermostat embedded under the tiles had only a sketchy relationship with the temperature of the bathroom.
The bathroom is the of course one place where UFH doesn't save you wall space compared with radiators, because you probably also want a heated towel rail to dry things on. So you don't actually make room for a piano in there.
[1] Tell me, bird of midnight ghosty,
What makes my toes so nicely toasty?
Quoth the raven, Underfloor.