Pardon, Not Expungement
I think what can remove the ill effects of a domestic violence misdemeanor conviction is a PARDON, a full pardon that includes gun rights. Only the Board of Pardons and Paroles of the State of Georgia can give pardons for Georgia criminal convictions. Well, maybe the President of the USA can do it too, but good luck getting his signature on that form!
I don't know what it takes to get a padon with full restoration of gun rights, but you could ask the Board or check their website.
Finally, I don't know if the feds would agree that if you're convicted by a State of Georgia court and later the State of Georgia's Board of Pardons issues you a pardon, you're no longer subject to the federal law, i.e. the Lautenberg amendment. They may take the position that once you're convicted, it doesn't matter if your conviction is later erased! That would totally go against the intent and purpose of having a "pardon" process in the first place. But who knows how the federal bureaucrats or the courts will rule? If they have already ruled and there's caselaw on-point, I am not aware of it (though I have not looked).
By the way, and EXPUNGEMENT is what you do for arrest records for arrests that did not result in a conviction. If you've been convicted of a crime and never pardoned for it, you cannot "expunge" the arrest from your criminal history report. At least that's how I THINK it works. Consult a real attorney [one in private practice and available for hire] who can do legal research for you as a client to get the best possible answer.