That would surprise me. I have never written a letter to the judge requesting a hearing. We file a Rule Nisi or Motions.
It sounds like you're about to mess up, and most pro se divorces either fail, have problems, or get delayed. It would actually be smart to pay an attorney for an hours time to review what you have done, tidy up any mistakes that may still be fixable, and then proceed.
Most counties do NOT have people writing the judge. I've done divorces in about 50 Georgia counties over the years and only one used letters as an option (the former judges in Clayton County allowed a letter, if it said the right things, to get judgment on the pleadings, instead of a formal motion, although even there, a motion was preferred. And recently at least one of their judges started requiring a motion and affidavit in lieu of testimony).
If a case is uncontested, probably 80% of Georgia judges will often do a judgment on the pleadings if there are no unusual issues, the paperwork is perfect, and you use a proper Motion JOP (and often that affidavit in lieu of testimony). Many of those judges do it only in attorney cases and will require a hearing for pro se litigants. Some only do it when no children are involved.
For courts that need hearings procedures vary. At least one county uses a stipulation to the active list. Some require a letter to the calendar clerk. Some want a rule nisi.
Since clerks CANNOT legally tell you what to do and friends usually get it wrong, and since you filed a case without doing homework (you never file anything when you don't know all the steps at the beginning), you really have hit exactly the reason you need counsel. Even in individual courts, the details you need to do can vary from judge to judge. But I suspect writing the judge isn't going to cut it.
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It doesn't have to be too formal, just let the judge know your agreement has been filed, if it has, and you need to schedule it for a final hearing. Clayton County handles more pro se divorces than most, so no one is going to freak if it's not perfect. Talk to an attorney if you need further help.
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