more concerns
hi ebeggel,
the pictures help a lot. A lot!
Your stone is 5' long and very thin and narrow. I might be worried about it cracking while being placed or if you have to pull it out to add more thinset... Do you know about trowel notches giving you a controlled thickness of thinset? Do you know the pillar method of setting stone? It gives you more leeway to play with (height) as you press it down into the right position.
I might thinset the stone onto a piece of Wedi board first, before placing it, since Wedi is reinforced with fiberglass fabric on two sides, and that makes it rigid. Then place the now-composite piece into the hole, and run less risk of cracking the piece now or later. Same principle as reinforced steel-and-concrete slabs, one component (which cracks but doesn't compress) on top, and another component, never cracking, on bottom, holding the upper component together. I have used Wedi, and steel too, to reinforce behind tiles.
You have enough extra space that you could put an electric heat cable under the stone. Very enjoyable. Cost is so low, it is less than a thermostat.
To hold the thing in place: if you use a little wood, as screed (and as frame) and a lot of sand mixed with cement as the real filler, you will have the best of both worlds.
I would not use Durock here, for a number of reasons. Doesn't necessarily reinforce the stone; might even make it more likely to crack. Using steel or Wedi will reinforce it.
When placing it, you could use "airplane" cable looped under it in two or three places to hold it and to pull up if ever necessary, and then pull the cable out when you are done.
DAvid