I don't know about QuickTime, but you can do it with Compressor. I don't have the exact steps but you create a droplet app which contains the settings you need. You can then drag and drop your files on the droplet and they will get converted.
What do you mean by 'FCP will not batch export to Avids codec'?
If you select QT (custom) from the format drop-down menu in the batch export settings window, do you not get the avid codec options in the settings drop-down?
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How to batch convert with Quicktime ??
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