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

In my limited expertise, I think the bandwidth over which shutters diffuse is going to be fairly narrow.

sounds like the decision has already been made

Install drapes that hang outside of/over the shutters.
Keep the drapes open except when you want to listen.
Tell your wife it is a necessary energy saving measure for the cold Minnesota winters.
Good luck with that.

Mitch2, great response! I will try this approach and idea.

Mitch's response makes me realize that the shutters could be installed on top of/over the acoustic window treatments I described (sound planks et al), so you could treat the window and have the look your wife is after. As others have noted the shutters themselves are acoustically transparent so there's nothing to stop you treating the surface behind them and getting the look you need. Heavy drapes will actually be very expensive so wonder if you should try something else before you spring for that?