I helped setup a system in a room that was 12x12, though it did not have many windows. We were able to get away with B&W N804 speakers although there was a 50Hz hump that was rather pronounced. But we used minimal room treatments... Were these speakers not overdamped, we wouldn't have been able to make it work at all.
I think the C1s are actually a great choice. They have a narrow dispersion pattern in the top end that will allow your windows to be ok, they have an overdamped bass response that only extends to 40Hz or so, and they have a fast bass roll off. This is about as good a combination as you can hope for for a room of your size.
Having said that, I would try to keep the windows behind your listening position and have the speakers toed in a lot - pointing directly at you is probably a good starting point. Also, carpet or a large area rug would be necessary to keep the window reflections in check.
However I disagree with your amp choice. The I7 favors bass response which is not what you will want/need. Many other amps won't be as difficult to work with.
I say go for it. Listening in the near field is a great experience and you won't need much power to get very satisfying results. I would look for a tube amp - a CJ should work great. Good luck and have fun.