Actually, there’s conflicting evidence on the forum about your chance of success. In November, Tristan implied it’s possible.
But less than a month ago, Leon reported no success.
Though in his case, he technically has one of the forms of photo ID but it was a big hassle to get it. So maybe Monzo weren’t willing to be as flexible. Either way, I’d send support a message and see what they can do. You can’t be the only one with this issue (and a search on the forum shows you’re not!).