Greetings, and welcome.
I've stared at your pictures for about five minutes now. While I'd like to tell you it's not hopeless, that is a very tough room, especially doing everything on the 45 degree angle with the TV in the corner.
Okay, that is a very large room acoustically. I am concerned about your budget, but I do think that the HK is an excellent choice. What percentage of your time will be spent listening to music? If you want satisfying music in that room, you may find that you need floorstanding speakers.
Likewise, to get satisfying home theatre, you WILL need a decent subwoofer, which will take up ~30-35% of your budget right off the top.
Placement is going to be really challenging. You may not wind up going with 7.1; 5.1 or 6.1 could be just as satisfying, not present the placement problems and help your budget. Moreover, I'm not sure how you could configure 7.1 in that room and get everything sounding great. All those angles are freaking me out.
I would strongly encourage you to put the front, main speakers (whether bookshelf or floorstanding) ON THE FLOOR rather than hung up above the windows. It's going to sound a lot better. Put them next to the fireplace. Just live with the idea of partially obstructing the windows.
What are you planning with the center channel?
The Axiom Full Metal Bracket (FMB) may really help you with the mounting. Do you have things wired already? i.e. are you stuck with some placement positions for the surround and rear speakers?
If your budget is pretty firm, I'd suggest the Epic Grand Master 175 package. Don't be afraid to order from the Factory Outlet if you can stand the wait. If you can spend a bit more, I encourage you to consider the M50's rather than the M22's. I don't think you should scrimp on this stuff; Axiom offers excellent value for the dollar, but even here, it will be practically impossible for you to get 7.1 for $1500.
I wish I could help more. I'm sure others will chime in.
You have a beautiful home. Thank you for sharing your project with us.
- Tom
