If you want to go whole hog, you should start thinking about a spoiler for your rear window. It's a good bet the angle of your rear glass is too steep for the flow over the roof to stay attached, and your trunk lid is too short to get the flow re-attached before it leaves the rear of the car.
(Tuft testing would tell for sure.)
So you're left with a trailing wake that's almost as bad as if it were a hatchback. A big mid "wing" (though not really a wing), about half to 2/3 of the way down your rear glass is something to think about, or a fairly high deck "wing" ...
But start with the easy stuff first. Sounds like fun.
(Photo to help folks visualize...)