Kind of along the same lines as you, I had to mount my TV above a radiator (probably in use a bit more than your fire, but turned right down with the other one in the room on high), but have a look at my thread and see what you think
Lounge Home Cinema Project
Looking at your wall, I'd take a centre measurement of the fire and use that as the centre line for your floating wall, and have equal distance of wall either side of that centre line, with the 'legs' of the wall running down either side of the fireplace. However, your fireplace is quite deep (15.5cms) and I think if you're looking at bringing the edge of the floating wall out that much, it's likely to look odd, so you'll probably find you still have some of the fire sticking out. (I used 34mm batons and 12mm MDF so not even 50mm deep. You can obviously get thicker batons, but would need to consider how the gap behind the wall that is visible at the side will look.)
I'd certainly look at having at least 20cms either side of you TV, especially if you're thinking about rope lighting - won't take too much away from the screen/picture, so an overall width for the floating bit of 131.6. As for the height, that's up to you. It will obviously be down to floor/skirting level, but leave a reasonable gap at the top to give the wall the effect you're after.
You'll be ok in concealing your wires as your wall will be at floor level, so just a question of either running trunking along skirting or replacing that section of skirting with a cable concealing version, or if you're unit is wide enough, they'll just run straight into the back of it.
Just a few of my thoughts for you to mull over!!! If you need any advice, I'll be happy to offer what little I have!!!!!
Good luck, let us have some more pics.
Greg