User blog comment:Rainb0wSprinklz/Problems with the final confrontation between Granny Rags and Slackjaw/@comment-3410662-20130101071232

To settle the disagreement without killing either of them, you'll have to exploit a glitch. Choke her out, but make sure to carry her instead of just letting her fall so you get her key. Bend time. Unlock Slackjaw; I've had the rats eat him if I just leave him. Teleport up to her room and slide the cameo into the furnace. DO NOT TURN THE FURNACE ON UNTIL TIME STARTS AGAIN. Wait for Slackjaw to finish explaining, then turn the furnace on and teleport out of the room. Save here, so you can try again if you screw up. When Granny Rags appears, wait a moment until the furnace starts glowing, then hit her with a sleeping dart. Instead of having her soul sucked out like she usually does, she'll slump to the ground, out cold.

That's how I did it.