Ok, well I think you have a good plan unless you wanted to talk about walling off the window
So, if you were to wall off your nook where the TV is sitting now, you would be able to create a closet to put all your components and have a really clean install. You would use IR repeaters to control your components. You could then mount your TV on that new wall which would be an advantage as it would be a little closer to your viewing position. Depending on the orientation of the joists in your ceiling, you may be able to recess the screen in the ceiling. Or you could just mount it to the ceiling. Then I would go with ceiling speakers to maximize the versatility of the space. You are not going to get the best "cinema" experience with ceiling mounted speakers, but with a good angled driver like this one
I think you would get a pretty good result. Surround placement will be a little tough, but I'm sure you can figure something out.
Alternatively, do the same thing but without reframing the TV nook. Less work and more or less the same result. I think the disadvantage for this first is the components, I like mine tucked away and out of site. Second is having the TV and Screen on different planes. That would nag at my OCPD.
Either way, I think you will get a pretty good result and 3k is healthy budget for a projector and screen. You can find some electric screens on eBay pretty cheap. I had one and it was decent for the money.
Good luck and keep us updated with your progress.