I import quicktimes quite often, almost exclusively using the Avid Meridien codec. I don’t know what kind of Avid system you are using, but each one has an Avid codec associated with it. Whomever is sending you these quicktimes needs to download the quicktime codec from the avid site, install it into the program they are exporting from, and deliver the quicktimes using that codec. You can alter the quality of the video/audio to conform to your size requirements.
Cheers