I'm having trouble matching up the photo with the floor plan, unless one is a reversed image. If I see what I think I see, I have no trouble deleting the gas fireplace and all that imitation stonework and installing a stove in its place, leaving the media center as is. Or, if you prefer, just reverse the location of the media center and the stove. As noted, go straight up through the roof with the exposed flue. Some people paint their flue to match the stove.
If you want to use wood as a primary heat source you can incorporate some helpful design elements. Insulate, insulate, insulate. The installed cost of extra insulation in new construction is borderline trivial. Think six, or even eight inch walls. If you must have that high ceiling (I'm not a fan - It is a lot of useless cubic feet that must be heated/cooled. And somebody has to knock down the cobwebs) then incorporate ducted air circulation into the design. Or at least ceiling fans. Use 36" or wider doorways everywhere. Make the door/passageway openings as tall as possible. With all the doors open you can get natural circulation through the guest bedroom, the bathroom, and on around the gym if the doorways are wide enough.
That glass wall is going to feel cold unless you have serious insulating window treatments. I had the luxury of building my house myself and chose fewer and smaller windows than is the fashion - and not without receiving criticism. Looking back, the one thing I would do different is to make the windows smaller!