As suggested, a normal screed overlaid UFH system is designed to use the whole floor as a thermal mass, it's the way it is meant to work. You set back the heating to warm the slab up in time for when its needed and that then heats the space above it. As long as it is insulated below the slab then all the heat will travel upwards into the space. You just need to get clever and work with it. It doesn't work like traditional CH/rads where by you turn it on and it starts to heat the space almost straight away.
There are other UFH system that do work faster (overlays) but again there is a further cost to that.
There are other UFH system that do work faster (overlays) but again there is a further cost to that.