avi export

I am editing in FCP X for satellite broadcast. The broadcaster only accepts AVI files. After completion of editing I allow all the audio & video to render before sending it to Compressor for conversion to AVI in clip lengths of not more than about 13 minutes each. My total video is always only about 25 minutes long. I then write the converted AVI files to DVD & to memory stick. The memory stick get sent in to the satellite broadcaster. My problem is as follows.

The converted AVI files all play smoothly on my Macbook & on the DVD but when the files from the memory stick are broadcast over satellite the movement of the subject appears jumpy/jittery. I was told that the only way to solve this problem is to take render the edited video from Final Cut to MOV format & then take the MOV file & convert it to AVI on a PC. It this true or is there a simpler/better way in FCP/Mac?