I had the same issue on a short doc I worked on.
My workflow for this particular project was a headache, was tedious, and the fix took just as long, for too long of a reason for me to explain right now,
MLV > MLV to DNG> AFTER EFFECTS > Export as Video > Import to Premiere
The sound was faster than the video.
The solution.
Recorded MLV in exactly 24.00 FPS. Timeline on Premiere was 23.976. Fixed that, but no dice.
Fixing it in Premiere doesn't do the trick, for logical reasons. You can't fix what's not there.
Kept thinking and voila. Go to the source of the issue.
MLV > MLV to DNG> AFTER EFFECTS > SET AFTER EFFECTS TIMELINE TO 24.00 FPS > Export as Video > Import to Premiere
The documentary was finished.