Please comment on your experience with Plantation shutters. Yes they look great,

You are dealing with two issues with plantation shutters, 1) Diffusion off the blades which will be infinitely variable over 180 degrees (you could spend a lot of time trying to dial that in alone) and 2) First reflections off of the vertical glass behind them which will not diffuse at all. Neither will absorb any sound which IMHO is  a much more important issue when dealing with first reflections.

 I think any control of the sound waves that you might obtain by varying the pitch of the blades will be lost because of the reflecting nature of the glass immediately behind them. Heavy toe in and/or heavy drapes which you can open close when listening to music would be a much better resolution.

Now if the plantation shutters/windows are immediately behind the speakers or the listening chair, that would be an entirely different situation and I think they might work fairly well in place of more audiophile type of treatments.

Well the only practice difference between shutters and glass, or any flat surfaced wall, is the slight curved nature of the blades will give a small but uniform  bit of diffusion. It won't diminish it - how that might sound I don't know. You are right though, it will be better than uncovered glass. If your speakers aren't hot on axis, toe in may still be the best solution