I don't know if they will respond, but I am going to attempt to call the Embassy in the morning. If they can't help, I'll follow the instructions on their website and consider it a "technical" error, and show screenshots of the married name in all its uses, then screenshots when they changed her name back to maiden name.
"I understand now (which I did not before) that the Green Card will beissued only to the name on the passport." .... I am answering only this statement with this post.
Assume that your wife's valid passport name remains as her maiden name.
When you filled out the Spousal Visa I-130 Petition, you could have used her married name as the beneficiary name ... where your marriage certificate is evidence of name change.
Also when filling out the electronic DS-260 visa application for NVC, you could have used her married name there as well as visa applicant, once again where your marriage certificate is evidence of name change.
If you had done either of the two things above in your document filings, her green card would have her married name on it and her passport would remain a valid document with her maiden name (thus always travel with the marriage certificate).