Converting a porch built on a raised concrete slab to a 3+ season porch. The walls, windows, doors, and skylights are in and are very weather tight. The final piece is the floor. I want to finish with tile and I want to add electric radiant heat under the tile so I can use the room on the occasional winter day. I have about 3" total depth I can use on the flooring. My plan:

-6 mil polyethylene vapor barrier bonded to concrete slab

-1" polyiso 4'x8' foam boards over

-1/2" polyiso 4'x8' foam boards over that, staggered so seams don't line up

-3/4" plywood (Plytanium DryPly?) floating over insulation

-1/4" Hardee/cement board screwed to plywood

-electric heater & tile over that

Questions:

- do I need plywood? Or can I use cement board directly over the rigid foam? If so, should I use 1/2" thick cement board? If so I have to worry about tile seams lining up with cement board seams, right?

- if I use plywood can I get away with 3/8" or 1/2"? Am I any better off with 3/4"?

- any better off with DryPly or similar "weather resistant" underlay?

- it seems to me that my set-up will pump heat into the plywood, the opposite direction I want the heat to go. Is it worthwhile to add some 1/4" extruded fan-fold type insulation between the plywood and the cement board? Or would this lead to cracking of tiles at the cement board seams?

- should each sheet of plywood be free floating on top of the insulation? Or should the plywood be bonded together? i.e. is it better to have 1 bonded plywood subfloor 8' by 8' or have 2 pieces 4' by 8' tied together by the cement board over the top of them?

Thanks much for any advice.