Hi Tom...You aren't kidding, that IS a difficult room. IF I understand your description correctly, it is almost an "infinite baffle" situation with reflective areas scattered around. I'm no expert, but I'll give it a shot.
You mentioned that mids and highs are fine, but you may want to try covering the glass doors on the right wall and the upper part of the stone fireplace as a trial, with a towel or blanket. This would sort of make the room "infinite" all around. Sometimes, with those frequencies, just keeping the levels approximately even from all sides is enough to make a noticable improvement. Also, if possible, I would move your main speakers out into the room (away from the wall behind them). Neither of these things has specifically to do with bass response, but you may be surprised with the improvements.
Now for bass response, I'm a BIG fan of twin subs...to the point that, lately, I would rather have no sub at all than to only have one. Although I've never had such an open space to play with, a room like yours may be a good place to try corner placement of two subs. In most rooms, I would only recommend this for HT and never for music, where I would suggest to pull them out in the same plane as the main speakers with unequal distances from the side walls. You lose some reinforcement this way, but the sound is much sharper. However, in a space as open as yours, the extra reinforcement may be a good thing. The good news is that, even with very cheap subs, you can hear the improvement from one sub to two...Soooo, go borrow the subs from two friends with HT-in-a-box systems, play around with one versus two and various positions to determine which setup gives you enough oomph, then go buy the best sub or subs you can afford to get the boom/bloat out and the crisp punch back in. Hope that helps.
You mentioned that mids and highs are fine, but you may want to try covering the glass doors on the right wall and the upper part of the stone fireplace as a trial, with a towel or blanket. This would sort of make the room "infinite" all around. Sometimes, with those frequencies, just keeping the levels approximately even from all sides is enough to make a noticable improvement. Also, if possible, I would move your main speakers out into the room (away from the wall behind them). Neither of these things has specifically to do with bass response, but you may be surprised with the improvements.
Now for bass response, I'm a BIG fan of twin subs...to the point that, lately, I would rather have no sub at all than to only have one. Although I've never had such an open space to play with, a room like yours may be a good place to try corner placement of two subs. In most rooms, I would only recommend this for HT and never for music, where I would suggest to pull them out in the same plane as the main speakers with unequal distances from the side walls. You lose some reinforcement this way, but the sound is much sharper. However, in a space as open as yours, the extra reinforcement may be a good thing. The good news is that, even with very cheap subs, you can hear the improvement from one sub to two...Soooo, go borrow the subs from two friends with HT-in-a-box systems, play around with one versus two and various positions to determine which setup gives you enough oomph, then go buy the best sub or subs you can afford to get the boom/bloat out and the crisp punch back in. Hope that helps.