That was how I initially approached them. I told them I made a mistake with my birth date and asked if there was any way to correct it. They asked me to send a photo ID with my name and birth date, which I assumed was to replace the old date. I then realized they meant the ID had to have the fake date and we went 'round and 'round (and 'round) on that until I gave up on them understanding what I actually wanted to do. Now I'm trying the more direct 'Please help me delete the account.' approach. I'm not hopeful, but you never know!
I think the more direct approach has a good chance. They can’t update your birthday, reasonably IMO, because they would be giving you access to the data after you failed the authentication. But they wouldn’t actually be leaking any info by just deleting the account.