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I must not have made myself clear. Sorry for that. I also have the 5GB iCloud plan. What I'm saying is, use iCloud to save contacts, email, calendars, etc. Photos take up an ungodly amount of space to save in iCloud. I just copy my entire camera roll to my computer to save the space in iCloud. If you use Photo Stream then I believe you need to use iCloud. But if you don't use that, then just manually save the photos to your computer. Then use AppBackup to backup up each app's data individually and then copy all that to your computer. I can send you a link to step by step instructions for AppBackup if you'd like. Once you have everything backed up, then DFU Restore as New to 6.1. Set up iCloud on the new firmware. Then jailbreak the phone, install all your apps, then use AppBackup to restore all your apps back to their exact previous state. If there are apps you haven't used in a while then skip the installation of said app. You'll always have a copy of the backup. For example, I have game saves from my 3G. Right now I don't have a lot of those games installed. But if I ever get the urge to play that game again, I just install it and restore the data via AppBackup. When I do that, it's EXACTLY how I left it the last time I backed it up via AppBackup. The good thing is, all of the backed up data doesn't take up a lot of space. So after I jailbreak a new firmware, I copy the entire AppBackup folder from my computer back to my iphone. Then as you install each app from the app store, you'll see it appear in AppBackup. All's you do is tap on the app, then tap restore. Once you do that, the app is back to the EXACT way you left it. AppBackup works for every single app in the app store too. iCloud is getting better at saving game saves and general app data, but its not a universal solution yet. AppBackup is perfect for this type of situation. I swear by that app. Plus it's free.
Anyways, that's just my opinion. Others will suggest iBye or PKGBackup. Those are fine alternatives too. I'm just familiar with AppBackup and have been using it for years now. I find it very easy it is to use. Good luck!
Edit: iCleaner is a very handy app. I always keep that installed on my phone and run it about once a month to clean out unnecessary junk. It'll get rid of a ton of stuff but I highly doubt that it will remove the 4GB of other. Like dhlizard and myself have said, the way you get "other" back to the smallest amount possible is to restore as new. I suggest you do a DFU Restore as New.