You could make it always-on-top send all the keys to Ozi, then make it not always on top. Depending on if your front end "minimizes" when you switch away or not, it might work fine even if you just leave it always-on-top.
Also, I think if you make it transparent it will stay on top. You can remove a color or you can make the whole window alpha-blended. If you don't want to do either, just make the alpha-blend 254. You will never notice 1-bit of transparancy.