try exporting it thru FCP and convert it in mpegstream. In mpegstream keep bit rate max possible and get the total file in desired size.
It just a workaround i am suggesting, generally its a bit rate which determines the pixel depth.
Yes proress is the solution.
Just for information – you will have same problem if you happen to edit/export VOB files as well.
I understand that files such as .mp4 or .VOB are meant for playback purposes and not for the edit.