Default [Q] Root Lost after 4.1.2 OTA Update What is the Best Practice to restore

I had rooted my SGS3 while on 4.0.4 using the stock Samsung rom and Odin without issue no custom ROMS were installed just root access. Early August of 2013 the OTA for 4.1.2 was rolled out and I had accepted the update which was installed without issue, which apparently should not have been the case (everything I can find says OTAs will fail if you have root access, but this was not the case). I now want to either return to a full stock to get the 4.3.3 update at which point I may remain unrooted, or gain root again and update to 4.3.3 with root. I'm cautious about how to proceed here since I've read about a lot of people bricking their phones while attempting to root after 4.3.3. My primary concern is that my flash counter is tripped at 1, but I don't have root access and am not sure how to proceed with out potentially damaging my phone. So I'm essentially getting the worst of both worlds (unable to receive stock updates from carrier, no root access to update otherwise.) and don't want to be stuck on 4.1.2 for the life of this phone. I still have SuperSU installed, but when I open it it says "There is no SuperSU Binary installed and Super SU cannot install it. This is a problem!"

I have searched these forums and a few related to it, and from what I can gather I should just reroot the phone following instructions for 4.1.2, but if I want to make the jump to 4.3.3 I wasn't clear if this would be needed or not, but none of the threads I could find directly addressed the issue for the ATT SGS3 i747. The closest I found was a thread posted last month where the OP was directed to the CF Root procedures, but there was no followup after that. I'm just a little leery about what might happen if I reroot with another method and end up with duplicate files/.apks etc related to the root process on my phone.

I also wanted to be sure that rerooting using a different method wouldn't somehow damage my phone.

Can someone with some experience please advise of the safest best practice for me to either recover root and update, or remove root and update so I can start fresh later? From what I can gather this should be an easy fix, but I would prefer to rely on the expertise of someone more knowledgable as opposed to winging it on a gut feeling I will be ok.