Yep, tried it - it works...

I moved out some furniture, pulled the projection screen down over the glass windows and movedthe rug to the middle of the room. There was a big time soundstage sensation. There are a number of other factors which I think contributed (eg, 2am listening at low level with lower overall acoustic noise floor and electrical noise floor) but the screen in front of the windows do work.
I guess the projection screen is not as effective as proper sound treatment of a think rug, but it will make a practical and convenient way to reduce the reflection issue. Many thanks Steve, for your keen observation. If there are other things I can work on, I'd welcome any input you may be able to provide.
George