Question: Is there a way to change the visual keyboard-theme via C#?
Or at least, some way to edit its properties, like background color etc?

Answer: 
Except for the `InputScope` (to open a numeric only keyboard etc.) and overriding key presses, there is currently no way to change any part of the visual Windows Phone keyboard.
Try changing ApplicationBar or maybe Systray background and foreground colors. I saw an app that had ApplicationBar and Systray set to white background and back foreground and the keyboard was black on white even with the dark theme. I think there may be a correlation.