Closer is brighter, but farther gets you more contrast. I opt for farther, but my room is pretty dark, but in your case it seems closer is better for brightness as well as ease. However, it is normally not recommended to use max settings, whether shift, zoom, etc, as you may limit the performance of the PJ.
I would consider a couple of possibilities. If you have the money, and it would cost a lot indeed, you can have a flat panel on the wall for ambient lighting, and a tab tensioned screen for lights off movies.
Or, perhaps, you can have two screens. You can consider a Dalite High Power pulldown screen, which is very affordable, to pull down over a fixed frame screen. Use the fixed frame for lights off movies, and the High Power for ambient lighting conditions. My guess-timate would be about $300 for 120".
The way the HP works is that it reflects light right back where it came from. So, in one sense, because the window is behind you, you will suffer just as much, most likely. Where the HP is excellent is with rejecting OFF-axis lighting.
When you have lights on in the room, keep them as far as comfortable from the screen itself.
You will never get the most out of your PQ with ambient lighting, however. Contrast is reduced exponentially with increased ambient lighting.
TO GET THE MOST OUT OF THE HP SCREEN, you will to have the PJ at the same angle as yourself, to screen, which usually means to have the PJ as close to the same height as your eyes. Doesn't matter how far in front, or way behind you, the closer the angle the better. Naturally, as ceiling mounted, the farther you mount the PJ, the closer the angle will be with your eyes to screen, which is what is desired.
The HP idea, as a retroreflector, works like
THIS.
Normally, screens work like
THIS.