yes as u seem to figure, u CAN NOT restore and jailbreak any longer becuz apple stopd signin for firmwares other than 6.1.3. Restorin will install 6.1.3.
What im almos 100% sure u can do tho is "Erase all Content and Settings" (i would do this twice or even more, jus to make sure it wipes everythin), wich wont install firmware. U shud look this up tho and make sure this is still the case, ie. in iOS6 "erasing all contents and settings" does not install new firmware and jus wipes all other data.
Then u will have a clean iDevice, wit ur current (6.1.2) firmware on it, and u can start a jailbreak from fresh. Once u JB, u WONT be able to do this again as it destroys the JB/system and ul be FORCED to Restore - to wutever Apples signin at dat point in time. So u wana do this before u JB. Again im not
100% sure this is still the case, but it shud be.
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Now In ur case i wud
definitely erase everythin and start fresh before doin a JB.. theres jus too much stuff on there and anythin can affect anythin and from my experience u want a JB dats stable and efficient, wich comes best and most often on a clean device wit a fresh wipe one way or another. A device lyk urs has a higher risk of havin problems.. I would back everythin up, Erase then JB and if u mus then restore ur backup.
Another proly better option is to save/backup ur game/apps wit iFunbox (or similar) -
http://www.i-funbox.com/ - then u dont hav to restore all 25gigs or wutever of data, u can jus restore individual games' or apps' data u want, hav the rest stored elsewhere for wenever, and not hav to restore a big backup wit all kinds of crap on a newly fresh JB. Not 100% sure it can backup Browser data, auto-corrections, SMS, etc. lyk iTunes, tho.
Plz Somone correct me if im wrong or unsure about anythin..