Panel placement for rear wall reflection problem

OK, I'll give it a shot. The reason that I didn't in the first place is that it is a very unique room. Standing in the middle of the room facing the speakers:
The right hand wall is basically all glass. It is about 15' long with four 7'x3' windows. The front wall is fairly standard, the speakers are mounted at the recommended height and width, about 8' apart. Between the speakers on the front wall is a fireplace. Above the fireplace is a TV alcove with a TV in it. The left wall gets interesting. To the left of the left speaker is a staircase, with a passthrough into another room. Then a 8' section of wall. The rear-left corner of the room is a hallway. There is no back wall really, it opens into the kitchen. The kitchen is VERY live acoustically. Lots of tile, glass, and counters. The room is carpeted. Two leather couches in an "L" shape, one against the 8' section of wall, the other out into the room.
So as you can see I have some challenges. One thing I am going to do is install heavy fabric vertical blinds to tame those windows. Other than that I'm just not sure.
Thanks for any help.

I would use the sonex or something thicker with a carpet over it for aesthetic reasons. Heavy drapes over windows are also very good.

Tough room - trial and error rules. The first thing you want to do is to try to deaden the first relection points as much as possible.I agree re the kitchen area being a major problem. Is there any way you can put something behind the sweet seat to absorb or deflect the reflections from this area, i.e. bifolding panels covered with heavy fabric, which you could fold up and put away when you aren't using them? Heavy drapes over the windows would be better than the blinds, but the blinds would be better than nothing, especially if when they are down they don't present a flat surface. On the 8ft section of wall on the left is their any space which you can treat (I like to use book cases filled with books of various sizes and irregularily placed)? Here is another trick to try which may not deaden the bright aspect of your room but could help with the clarity of the highs because it lengthens the time of arrival of the first reflections (and its counter intuitive as well as strange looking at first.) Play with the toe in beyond the normal "straight ahead to slightly pointed in". Cross the axis of the speakers in front of you 'til the axis of the speaker is pointed somewhere between your head and the adjacent wall. This could also help fill in the center of the sound stage and widen the listening position. Sorry I couldn't be more helpful.