Wow, I don't see a difference at all, unless the mismatched wood comes all out the way out to the area outside the picture you posted.

Unless these doors are constantly being opened, I'd just find a great rug to put down. Alternatively you could sand the "different" area and restain it to match. If this is true hardwood, it is probably about 1/2-1" thick. You could always cut the area out and lay the stone so there is no higher edge to it.

If it were me, I'd just get the rug, LOL.

I would suggest either a 2" to 3" thick "slab" of quartzite to match the veneering (same thickness and material/edge detail) OR a warm grey slab of precast concrete. www.pacificstone.com or www.stepstone.com has a good selection of these types of things. You would probably order a wider wall cap material and have one edge cut off to sit flush up against the existing firebox. Good luck!

I would put a semi circular rug in front of the fireplace and two huge floor pillows on either side of the fireplace. Good luck.

Another question... is it a functional fireplace? If so, is it wood burning or gas only? Flammability is a real concern in considering the material selection directly in front of the box.