So the source movies are .dv (or .mov) with no other important metadata than the date in DV:DateTimeOriginal, right? If that is the case, you can (first do a test with copies in a folder):
Copy the date one-by-one (you have to modify the source and destination file names accordingly):
exiftool -m -overwrite_original -wm w -api QuickTimeUTC=1 -api LargeFileSupport=1 -tagsFromFile source.dv '-AllDates<DV:DateTimeOriginal' '-Track*Date<DV:DateTimeOriginal' '-Media*Date<DV:DateTimeOriginal' '-FileCreateDate<DV:DateTimeOriginal' '-FileModifyDate<DV:DateTimeOriginal' destination.mp4
Or, as a batch for all same name .dv same name .mp4 in the same folder (change .dv suffix in the command to .mov if that is your source. If both the source and destination are .mov, it is easiest to have them in different folders):
exiftool -m -overwrite_original -wm w -api QuickTimeUTC=1 -api LargeFileSupport=1 -tagsFromFile %-.0f.dv '-AllDates<DV:DateTimeOriginal' '-Track*Date<DV:DateTimeOriginal' '-Media*Date<DV:DateTimeOriginal' '-FileCreateDate<DV:DateTimeOriginal' '-FileModifyDate<DV:DateTimeOriginal' *.mp4
Then optionally rename the .mp4 movies via their metadata dates (filename looks like 2001-0101-1200-00.mp4 and will append _NUM if CreateDate is the same for multiple files):
exiftool -m -P -fileOrder5 FileName -api QuickTimeUTC=1 '-FileName<QuickTime:CreateDate' -d '%Y-%m%d-%H%M-%S%%+2nc.%%e' .