Combining with this idea: Harry openly speaks about Patronus 2.0, everyone's Patronuses fail (especially the sparrow and squirrel currently guarding the Dementor, everyone would see them fail), Harry casts his Patronus to protect Hermione (or she figures it out and casts her own, not that she would get the chance to but she might figure it out at least), and the Dementor starts sucking souls until Lucius retracts his sentence.

Heck, maybe even threaten to spread Patronus 2.0 to the media, make wizarding Britain's animal Patronus population fail, then Aurors won't be able to keep their Patronuses up to guard Azkaban. So even if Hermione gets in, she wouldn't get her happiness sucked...