I like the nautical idea, not sure I'm picturing exactly what you mean. I'll have to search for a picture.

do you ever get direct sun? and how much privacy do you need at night?

The windows have a film but we get some direct light. Privacy is not much of a concern.

I love the look and sensation of light gauzy simple white curtains, of a muslin weight. They move gently in the breeze, and are just so pretty. We had a sunroom like yours years ago, and did just that, and they were very pleasing, very calming. If they got grubby, I popped them in the wash and then hung them while still damp, and they blew dry in the breeze - no ironing required!

woven wood roll down blinds are nice too, they let the breeze through but if you are looking for some softening when they are rolled up they wont help much.