Hi there, not a pro but i handle special order blinds for window treatments where i work. A 2” blind will be heavy looking on those windows when you need an outside mount, although when these are ordered for outside window frame placement, there should have been an option for outside returns for your valences. That would cover your headrail and ‘wrap’ around and ‘return’ back to the wall at a depth of your choosing. If you might consider another type of window covering, a roller shade or roman shade with a ‘flat’ fold might not be to ‘thick’ looking when completely open. If you still prefer to tilt a shade open and raise, there are 1” thick and i believe 1 1/2” faux wood slats available for order that would be a softer look.

Another thought for this room could be plantation shutters, not as budget friendly but they are great insulators and increase home value. The shutters have a wider slat which looks nice because the wider the slat, the less slats, hence more view when open. I would stick with white IMO for the simple fact if you ever change wall color, decor etc, no harm no foul. You may even be able to add cost of shutters as energy efficient home improvement, if you are lucky enough to get to itemize on your tax return :)

I wouldn't just put blinds on the windows. I'd put blinds and then curtains. If you do this, then maybe the head rail from the sides will be hidden.

I agree with shirlpp.....no stand alone blinds. Adding curtains will create a warm and finished look.