I am planning on applying a tint film to reduce the heat entering the house in summer as well as reduce damage to the floor and furniture, but the Australian sun is so harsh it requires a lot more to block it out :(

Absolutely you can mix traditional windows with contemporary window treatments, although I don't think plantations are considered contemporary by any means. Ordinarily sash windows can have shutters installed over them, however I can see your sill is very narrow given your bottom pane sits forward of the frame. I can see privacy is no issue, in fact you have a great view and half height windows allow light in and keep peepers out, so I suggest plantation shutters fitted to your French doors, to allow tilt and directional light and a roman blind as the folds of fabric mimic the frames themselves to your corner arrangement. If they are too fussy for you a standard holland blind, however be creative, you can have a bonded holland which allows for a fabric front bonded to a block out backing, you can ask for a roman fold on the bottom making them look like a roman when rolled almost all up, and dress the window a little better, but Hollands can roll up into the frame and allow for maximum window when wanted.

Love this idea... some images for inspiration. If black is too harsh you could consider colorbond colour Monument

Maybe use a Hardi product which imitates timber so you don't have to re-oil every year Personally I like the shutter system you have as it looks like a beach house If window treatments are dark it will darken the interiors as well, due to reflection Make the lower section of the building light & use the same colour for the existing shutters - maybe with a stripe (e.g. white with light grey) Then have the grey as the top part of the building Trim with white & a darker grey