I understand why you might want these, but honestly...I don't love this. Those windows are great, and since you need neither privacy nor light control, I think they should be left alone to allow them to "disappear" so you focus on the yard beyond. To me, curtains call attention to windows, not views. You're right, they have to be floor-length, which means they'll interfere with the couch. And the rads. When will you ever close these? When you move the couch? That said, we did the curtain track route in one of our rooms, across a 12-foot room. (the post with pictures is in my clippings.) If you get an unlined (we used sheer) drape, they stack back to practically nothing. And if you want to get super-crazy, you can drywall in the track to make it completely invisible. They definitely add softness to that room (our master), which is pretty much cool blues, whites, and angles. But we did it, in the end, for privacy. What about doing something else to add a warm and finished look to the windows? Like some lovely thick wood windowsills? I haven't googled or flickr'd around, but I think I might be more into something using wood to add something softer than white wall to that view. JMO, I know whatever you do will look gorgeous, you have great taste!

We are not window treatment people either, but have started to add some as we've reno'd/decorated a few of the rooms in our house; two bathrooms and our office. They really do help to finish off a room. That said, we're not covering our kitchen bow window, or the DR bow window, though I might consider something for the DR window at some point--just for the window panes themselves, not to cover the whole bow-unit. We used Hunter Douglas' Designer Screen Shades in the Roman Shade style (ours are mounted inside the frames becuase of our window style/frame depth). The shades are very clean-lined and range in sheerness. With the sheerer weaves/fabrics, you can see outside with them down and they allow a lot of light in.

Making a tree? That’s awesome. You sound quite creative so here’s a thought. Why don’t you use plain shades, as the others have suggested, and paint your window trim the wall colour, so it all just becomes background. Then you could paint or buy a simple mural (branches, vines, woodland stuff), and flow it right over the sill and trim, on the wall? With a 3D tree, it could be quite spectacular. I’m not exactly sure what your theme is, but you could even hang stuffed monkeys, birds, fairies, etc. (whatever suits your design). Here are a few pictures: Jungle https://www.houzz.com/photos/jungle-room-tropical-bedroom-chicago-phvw-vp~270556 Garden https://www.houzz.com/photos/little-girls-bedroom-traditional-kids-minneapolis-phvw-vp~112598 Monkeys https://www.houzz.com/photos/eclectic-kids-eclectic-kids-raleigh-phvw-vp~1176668

There's no other way to arrange the furniture? If you post a floor plan (hand drawn is ok) showing measurements of furniture, walls, window width and doors, maybe there is another solution. But if you don't want to do that, I'd just get some nice looking shades of your choice (bamboo or roman) and not worry at all about covering them with draperies. Depending on the size of your window, you might have to outside mount (better for light control, I think), because to inside mount might require a custom size.