It would be really helpful if we could at least sort PMs by sender. It's nearly impossible to manage without search/sort.
Your best bet is to use folders and separate & segregate according to your needs and whims. Though, if I'm not mistaken PMs have self-destruct timers on them. I do not think they will add this kind of functionality though. Your best bet would be to petition vBulletin.com to make such changes in a future edition.
Download them all by the buttons at bottom on PM page. Its easy to search in the text file than opening each and every PM of 1k.