m2t is not an editing codec and it is highly compressed (mpeg2 in a transport stream basically).
I don’t know the AVID you refer to so I don’t know what other options you have to export. To solve the sync issue though, you might be better exporting the audio separate from the video and resyncing in FCP.
In the past I have had issues importing an AVID generated QT file which was supposedly Apple uncompressed 4.2.2 but it looked weird. The facility with the AVID somehow fixed this, probably by using third party software, to take the uncompressed from AVID and make a Blackmagic uncompressed QT which imported fine.