I can suggest only 2 things:
1. Post some screenshots(or a video if possible) on the FTL forum, so I can check it out.
2. If you are using jrb's launcher. Try running the game without it.
Just download the archive, extract it and play. Then tell me if the problem still occurs.
Cuz jrb sometime ago was messing around with client resolution, which is not yet fully supported.