I don't follow you, the comment about copying everything from the previous backup to the computer, and importing it into iTunes. All the info, both what is on my old phone and what I want on the new phone, is either already in my iTunes library, or it would be sync'd, like my contacts from the Address Book, photos from iPhoto, etc.
The full sync is already almost done, I have just over 20 Gig of apps, songs, and videos to sync. The songs take the longest, but it is taking less time than I thought it would.