ply with a hardiebacker 250, and a decoupling mat, would be my way to go. There may be an initial lag in warm up time, but as long as your floor is free from deflection it's a price worth paying imo
I have done a similar thing in my house but the floors do not get very warm cos you are right the wooden floors are a good insulator. Have you looked at something like the Celecta Screed Board which is a gypsum based board which is a good conductor.
Another option I have seen used is a metal diffuser plate rather than timber boards. Alluminium is good for this.