I think I accidently found a way to get apps into the correct folders with iOS 6.1.1 and iTunes 11. I backed up my iPhone 4s running iOS 5.1.1, transferred purchases, and then restored my iPhone 4S with iOS 6.1.1. After the backup completed, the iPhone restarted and started syncing applications from the Mac onto the newly restored iPhone. I was not watching this proces, and when I got back to the Mac, I got confused about the Mac application I was looking at, and couldn't find my iPhone in the left-hand side bar (which I had enabled to look like all previous versions of iTunes). Then, I unplugged my iPhone from the Mac, and only at this point did I relize that the iPhone was syncing apps when I pulled the plug on it. So, I plugged it back in, wondering how I can re-initiate the sync of applications back to the iPhone. iTunes 11 no longer has the check box to get it to sync all (or checked) apps to the iPhone. Instead, there's a "remove" or "install" button next to each app in iTunes. So, I decided to "restore from backup" again, and this time, when the iPhone restarted, I made sure that it downloaded (synced) all apps from the Mac. Strangely enough, all apps were in the correct folders once the sync completed.
Today, I upgraded another iPhone 4S from iOS 5.1.1 to iOS 6.1.1 by backing up, transferring purchases, then restoring the iPhone, and then selecting the backup. This time, when the iPhone restarted, I did not interrupt the syncing of apps, and let it run all the way until all the apps were synced. To my chagrine, all the apps (more than 100 of them) were scattered over 6 screens and not in the folders where they were supposed to be. There were no folders (except standard ones), either. Moreover, when I manually moved all the apps to the correct folders (while my iPhone was plugged in to iTunes), I then clicked on the iPhone in the left side bar, and iTunes prompted me with the message that the iPhone settings (or something to this effect) have changed and if I wanted to accept the change. When I answered yes, all of my work was undone and all the apps were again outside of the folders with all of the custom folders gone (just like it was after the initial app sync following the restore from the backup). I then had to spend another hour re-doing my work. This time, I unplugged the iPhone from iTunes while moving apps into folders. I think my next step will be to delete the backup from iTunes and run the backup again and then transfer purchases because when I plug my iPhone into iTunes, the latter does not reflect the way my apps are arranged on the iPhone. Again, there's no more Sync with iTunes checkbox (in iTunes 11) mentioned in this thread, so it's unclear to me how to get iTunes 11 to recognize the new layout of my iPhone besides wiping out all backups and backing up my iPhone as though this were the first backup. I have Time Machine backups of my previous iPhones' backups, so I can always go back to Time Machine and restore the backup from there (if I have to).
But, overall, this is a great shame that so many years of people complaining of this feature (ever since folders were introduced in iOS) - iOS 4? - Apple has not fixed this issue. I guess the backup and restore (with app syncing) was designed for the earlier iOS versions that did not support app folders, and Apple never modified the code to allow users to not only restore the apps, but also restore their location inside custom folders. What a shame!