I am having the same issue and after reading your post, I changed the compressor settings for the MP4 to 30 key frames but still had the same issue of it going out sync. Basically the video would start playing in slow motion. I made the MP4 from a Quitctime export, not directly from FCP.
Any suggestions? I have never had this problem before. I am making final outputs for a client for final approval and am really surprised to see this happen.