Quite enjoy hunts as they are, and would be thoroughly put off if they did sync them.
That said, the fact they despawn is horrible.
Would seriously consider leading a train were it not for that.
Been on trains where every other mark has vanished, would never want to be in that position.
If they have to despawn for server reasons or whatever, at least put some in game indicator as to when. Maybe a debuff on the mob that does nothing more than tick down to when it's set to despawn.