You haven't told us what your fcp sequence settings are, but here's a workflow that will solve the problem (I hope). I recemtly had a similar experience but with a green line.
Export a selfcontained quicktime with current settings from fcp.
Bring this file into compressor. In the settings window at the top right, hit the + and create a new mpeg4 setting. Here's the trick. Go in to the geometry panel and set the dimensions to 854 x480. For the best quality, go into the frame controls panel and set the resize filter to best.