How to start the Dark Brotherhood without killing Grelod the Kind

Let's talk about how this quest actually works internally:

• Grelod has to end up dead by some means.
• Grelod has 1 hit point, so any damage whatsoever will kill her.
• Children are immune to damage, but Constance is not. Attacking any of these people is a crime.

Here are some options I can think of:

• "Accidentally" summon an unbound ash guardian (from Dragonborn), allow it to kill Grelod, then kill it before it can kill Constance. This is challenging because Constance only has 30 hit points. I'm unsure whether you'll be held responsible for its actions, as the ash guardian spell is implemented differently from standard conjuration spells.
• Summon something else, then hit it until it turns hostile. It will probably also attack Grelod if she's in range. But it might attack others, and you'll be held responsible.
• Summon a flame atronach and kill it within range of Grelod. You'll be held responsible if the plume hits anyone other than Grelod.
• "Accidentally" hit Grelod with an area-of-effect spell such as Fireball.
• Cast a frenzy spell on Grelod, or reverse-pickpocket a frenzy poison with the relevant perk. Don't cast it on Constance, or it will be considered an assault.
• Tell yourself that you're just "roughing her up" by hitting her, and then pretend to be surprised when she dies of a punch to the face.