Reviving this old thread because people have been DM-ing me. So here it is:
Changing the assigned embassy to a case is quite common and can be done by a simple public inquiry https://travel.state.gov/content/travel/en/us-visas/visa-information-resources/ask-nvc.html .
Your request can be as follows (this is how I did it myself):
Dear Sir/Madam,
I would like to request a change of venue to the U.S. Embassy (OR CONSULATE GENERAL) in DESTINATION CITY Y, DESTINATION COUNTRY X. I am a citizen of DESTINATION COUNTRY X (OR A COUNTRY Z WHICH CITIZENS ARE ALLOWED TO BE INTERVIEWED FOR IV AT COUNTRY X), so I am eligible to undergo IVP in CITY Y. I have included a copy of my passport and birth certificate with certified translation to support this request. Thank you for your time and consideration of this request. If you have any questions or concerns, please do not hesitate to contact me.
Attach your petition approval notice and passport+birth certificate+translation to this request in ONE pdf.
Check the https://travel.state.gov/content/travel/en/us-visas/immigrate/nvc-timeframes.html under public inquiry response time to get an estimate of how long you should wait for a reply. You will realize your request has been accepted once you see that you cannot log in to your CEAC with your case number! That's when you know that in a few days you get your new case number in an email.
Is it possible for your DQ date to change? There is a very very small chance it changes (we have had very very few cases like that in a thousand member group that I am in, with probably hundreds of transferred cases). This change would be against the rules of NVC!
But the NVC officer may not know about it and that's why they do it.
You will realize that has happened once you get your new 60 days notification from NVC, which states your DQ date. IF for any reason you do not get that notification, or you get it and it states a different date, immediately contact NVC to ask for confirming your DQ date.
If the DQ date has changed, you can fix it back by contacting the NVC, and explaining to them your situation and that changing embassies should NOT change the DQ date by NVC rules. (and yes, we have also had cases that successfully fixed their DQ date back to what it should be).
Have patience (a lot) and best of luck with your transfer.
P.S. You don't have to wait to make this transfer. In fact, You can make this request after your case has been created at NVC, and before you have even submitted your DS260 (so even before you get assigned a DQ date!). And that's what I'd suggest you to do. I myself submitted my request after mailing my civil docs with the old case number (I have to mail because my case is EB) and before getting DQ'ed!! I didn't even give a headsup to NVC ! but the officers were surprisingly organized enough to send my DQ letter and new case number in one email!
Lastly, In case you have not sent/uploaded your civil docs and are making this request, they may also send you a new coversheet for the submission of your civil docs (if your case is EB, then you have to attach that to your mail). If they don't, then use the previous coversheet but strike the old case number and attach a letter explaining that your case number has changed but you did not receive a new coversheet, hence why you are using the old one.
Hopefully this should answer any and all questions (and I won't get a DM anymore ) .