Don't sand the fuselage, unless it's shape is incorrect.
Strip styrene is what I would do. I would at the strip to the bottom of the stabilizer, then test fit. Add more strip if the gap is still too big, sand the strip if it is too much. Sand and test fit and sand again. You may have to sand/scrape the edge of the strip to be flush with the sides of the stabilizer. When you get a good fit, you can glue it in place.
To answer your first concern, I agree that it does need work.