I'm by no means an expert and your budget is beyond my means however I had the same problem with corners and girlfriends as you. My solution was to offset to the corner and run the Auto setup function on my amp. Then I sat down and watched clips of James bond films on Blu Ray. The car chases, gun fights and the theme music I found very useful for getting the balance of all the speakers. The sub is perhaps the hardest to integrate well but play some R&B and if you have it turned up too much it will be very apparent.
The left is crammed in the corner next to the TV. The center is slightly offset under the right hand edge of the TV with the left and sub down the side of the Sofa. Cinema buffs will have a fit over the speaker placement but a lot of people have no choice.
The rear placement I found the hardest and contrary to some advice I found it best when they pointed directly at the listening position. the stands are a DIY and are a work in progress. Photo taken from fireplace. (lager glass obviously an important feature that took a long time to get right)
Speaker cables are easily hidden under the carpet. I payed a fitter £30 to come in and run the cable around the edges of the room. All they do is slice out a slither of the under carpet. I had normal round speaker cable and I can't see the difference but you can buy flat cable that is even easier to hide. I would factor in a fair proportion of your budget for cables, especially HDMI if you don't already have them.
I went down to sevenoaks and told the man my budget and gave him a diagram of my room. He wanted to sell me KEF eggs because of the space( which in hindsight would have been better I think) but I wanted floorstanders and he adapted to that. He made me a cup of tea and sat me in their test room and we spent all day testing various things out and discussing the details. Despite my smallish budget they made an effort and I was happy.
True a dedicated stereo player will always be better than a similar priced AVR at playing music however I would suggest that only the serious music buffs will be unhappy with an AVR's stab at it. The benefit of an AVR is that most now have loads of features that your TV or BD player might not do ie stream iplayer or upscale DVDs.