Thank you for contacting us for assistance with properly moving characters between worlds on your account. We understand that there are limitations and congestion issues, and this can cause a number of troubles we would like to help you resolve.

Having reviewed your request and your account, we will be able to assist you with transferring your characters according to your request. However, we would like you to understand and agree to the following restrictions before we process this request:
*The amount of gil that can be transferred is limited to 3,000,000 per character and 1,000,000 per retainer. Any excess gil will be removed upon transferring.
*Items cannot be for sale on the market, sent through the delivery system, or entrusted to the Calamity Salvager. Any items meeting these requirements may prevent a successful transfer or be lost. We cannot recover items lost in this manner.
*Your character cannot be enlisted in a free company, holding a free company petition, or signed to a free company petition. Not meeting this requirement will result in the request being denied.
*You must be logged out of the game for the world transfer to be processed. Should you be logged into the game when the world transfer is processed, you will be logged out of the game to process the transfer. This may interfere with any task you are working on at the time. Being logged in may result in the transfer failing.
*You must be outside of any instanced areas. Being in an instanced area may result in the delay or denial of your request.

If you agree to these restrictions, and have made any corrections to meet them, please respond to this ticket or send a new ticket noting your agreement, and we will begin the world transfer process. This process may take several days to complete from the time you submit your response.

Thank you for your patience and understanding, and we look forward to hearing back from you.
Final Fantasy XIV Support Team
This is the response I got from them recently. However, I've personally already remade my character (though with great irritation at the time) and have no need for their help anymore. I feel better that they've taken the time to look it over and actually offer to help though so that's always good.

I'm posting this here just so people who are/were having an issue can try and get it resolved too. All I did was reply and explain to the auto-response email I got after submitting the problem to the support team. Now, obviously since I don't need the transfer anymore I can't verify if they really will go through with their offer but it's better than nothing.