Wow, lots of great replies. What a great forum. Thanks to all.
As I suspected, the room is going to be a big deal, as confirmed by many of you. Unfortunately, there's really nothing I can do with the rear windows. They are huge, cover the whole wall, and really make the room a special place. Nobody in my family would agree to cover them just so the sound can be better, including me. (I know that's heresy. Sorry.)
This all leads me to the conclusion that this is never going to be great sounding so why go over the top with Genelecs? Originally, I had decided to go with KEF LS50 Wireless II plus a KC62 sub. In fact, I bought those and haven't deployed them because Christmas and a trip got in the way. (If I go another way I could easily sell them well, especially since the LS50W2s were on sale.) So many people tout the benefits of the built-in amps on the KEFs that I really came to believe that there was no way I was going to do better with passive speakers and an amp without spending tons of money. So this is what led me to the Genelecs too: built-in, purpose designed amps. Same thing as the KEFs only better. Then that led to the whole room correction obsession.
So there are really two things at play here... the concept of room correction and the concept of active speakers. If I'm willing to forgo the active speakers, I really like the suggestion made earlier in the thread of the Lyngdorf TDAI-1120 plus passive speakers. That device would be extremely convenient for my use, and it has good room correction apparently. I also have a pair of B&W 805-s speakers that I bought a while back that I could pair with that. Then maybe use the KEF KC62 I've already got.
So, to change the direction of the thread, I wonder which would be better:
1. KEF LS50 Wireless II + KC62, giving the benefits of active speakers but not so much room correction or...
2. Lyngdorf TDAI-1120 + B&W 805-s + KEF KC62, giving the benefits of room correction but not active speakers
Given my room, am I going to get more benefit out of the active LS50s, or out of the room correction in the Lyngdorf, which probably can't really fix the biggest issues in my room?