imei/efs: downgrade to ICS 4.04? topic

Hi, I have the IMEI/EFS problem, and I have read the main topic posts on the subject, and although very informative, most of the possible solutions are beyond me, other than send for repair which I am holding as a last chance solution. I am now thinking I should downgrade to ICS 4.0.4, then root the phone and then backup my EFS folder. Currently I am running 4.1.2 with 0049xxx imei and getting not registered on network. My i9300 is unlocked but has never been rooted. Would a downgrade to 4.0.4 be feasible?

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