And you have one more burden: determining how much footage of pipe is under the cement. If your system is old enough to be copper, you may have several times less surface area than what would be installed today with PEX. Those systems were often unable to keep up on cold days and many were disconnected. Builders started being cheap a few thousand years ago.
I worked on a system with new pex over the existing slab, then we poured mortar over that and troweled the finish surface to a texture and stained it. Works great except you must raise all your doors and etc. for the height loss. You can even add a thermal break under the new assembly. Not easy unless you are gutting the house.
Again, you lose a lot of radiation by adding wood over it all. If you insist, use the thinnest wood system you can find.