Flooring – Tiles on underfloor heating

Usually 3 zones is plenty for a single story structure of this size. In this case I think your contractor has given you good advice. The distribution is to like living areas which is good. Obviously, more zones allow more flexibility and control, but the costs of equipment and labor rise as more zones are added.

We have a water based underfloor heating system fitted under wood (old pine I think, not oak) floorboards which works fine.

It will be less efficient than a tile or stone floor as wood has lower thermal conductivity than stone or tile. You would have to fit a more powerful heat source to gain the same temperature gain in your room. It might even be the case that you can't get mats that are powerful enough - the water pipes we have are too hot to touch with bare hands - if you had enough current to produce that amount of heat you might be in danger of melting the wires.