“The reason I used premiere to sync is that the video files that had a reference track, had very low volume and where clipped at the same time.”
Perhaps you could have done same in Avid, I don’t know, I don’t usually have to do the syncing, but it’s worth a look.
So did they not use a slate/sticks for the footage? If yes, and you can’t sync automatically using waveforms or timecode, it’s not that time consuming to mark the sticks on both picture and sound in Avid then using ‘auto sync’ > ‘sync by inpoints’ to create your synced clip. Map a key on your keyboard for the ‘auto-sync’ command to make it faster, then select each picture and audio that goes together, hit your mapped key and repeat for each clip.