Properly working with vector files
Ok, so I solved it myself, and it wasn't pretty.

To be able to work with my vector file in Davinci Resolve 12 (and in Final Cut Pro X without loosing any detail), I first had to convert it into a font. Yes, you read that correctly. I had to create a font where I assigned my logo to a specific character and then use the font in my editing program.

More specifically, to achieve this, I used the excellent Icomoon web app where I could import my vector image, assign it to a character code (in my case, I used "30", which stands for numeric zero in standard UTF-8 encoding).



Then I simply downloaded my font, installed it on the system as any other custom font, and accessed it as a text object in Davinci Resolve 12.



What a time to be alive!