Try sitting her in the sling with her feet sticking out. I can't really explain that, but basically so her bum is on the bottom edge of the sling and her feet are dangling, but the bulk of the sling is firmly supporting her back. Pull it nice and tight and she won't fall out.
Try resting her on one of your shirts (unwashed) while you feed her to sleep so she has your smell with her when you sneak away, and put a nice big photo of your face in front of her so when her eyes flutter open she'll see you and go back to sleep.
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