yeah google says it's possible but different websites say different things about how to go about it. Hopefully someone who has tried it before will chime in
naw, it worked out in the end as one eventually took pity on me, but they were insistent that it was too late for a ticket out and wouldn't believe that it was sincere
Update: after a few hours, one of them took pity on me. Not sure if that was always the plan to make me sweat and appreciate the seriousness of immigration law, but it worked.