Dual 7950's would be good but your processor might bottleneck not sure. You may want to sell your cpu, mobo, and video card and combine that money with the $600 for a Z77 board, ivy bridge cpu, and better GPU whatever those may be.
The dual monitor does not affect anything. Gaming will not be impacted.
I suppose you could market your GTX560 and attach your side monitor to the GT240.
I did that once, but found absolutely no benefit in gaming to offloading the side monitor from the main graphics card.
If you do not already have a SSD, my suggestion is to use about $400 on a GTX670, and $200 for a 240gb SSD. That will be large enough to hold the os and a large number of games.
If you are looking to win benchmarks, sli might look good. But, there are too many issues involved, and the real performance benefits will not be apparent when using a single monitor.