Shutters sound like they would be a great addition to your new almost at the beach house. Is it an open concept? If so while you can change things up a bit you'll want to repeat some element and ensure that everything looks great together. Even the rooms you're thinking of putting drapes in might benefit from shutters or wood blinds for both looks and light/privacy control. Also be aware of how these windows will look from the outside. When choosing fabrics look at your existing furniture for inspiration or a piece of existing art or if buying new furniture think about the windows as you do. Everything in the room ties into each other. Ideally you would have swatches and samples of every finish in the room from flooring to window coverings and everything in between including wall colour, area rugs, bedding ect to help make your final decisions easier.

Catherine the panel blinds could be your solution. They are available in sheers, patterned, mixed etc and operate on a track system. It's an update of the verticals that a lot of homes have. If you have Ikea in NZ you could sus them out there.

Nothing will affect the feel of your house as much as the quality of the light. If you can at all swing it, keep your divided lights. Looking at your photo, those windows are gorgeous. Can you place glass on the exterior? I have some lead light windows in 2 locations. I made new frames with the leaded old glass on the inside and plain glass on the outside. While not as weather-tight, it's much better than single glass. While not as neat as your present windows, the new windows that have the interior and exterior lights with the spacers between the glass also look great and are at the present standards for energy efficient. We live in the PNW and used Milgard; less expensive than Anderson and Marvin, but so far I'm very happy with them.

I grew up with these panel doors and remember the glorious day they were replaced by a curtain. So if you are open to the idea, for ease of use, least effort and cost that's a simple fix that your daughter may want herself. The top cabinet doors can be considered a cornice for the drapes, and can be upholstered, maybe in the same fabric as her window curtains, and a simple drape with coordinating stripe on the bottom. Search "upholstered doors" on Houzz, and you will see ideas for nailhead trim, tufting, etc as well. You may also be able to add thin trim molding in a custom design to make them special. Good luck!