I think that if they go the "Princess Consort" route (I hope they don't), they'll just issue a press release stating that "HM the Queen wishes to be known in public as HRH the Princess Consort." It avoids any legal issues and doesn't create any precedents for future monarchs. In the event of any official paperwork talking about her, it would still call her the Queen, etc. Yes, she'd be the Queen, but no law demands that anyone request to be called the Queen.
They cannot do as you describe without raising serious constitutional issues, including the precedent of 1936 with Edward VIII. She is automatically Queen and any variation requires consent from Parliament.