It might be a bit of a pain, but have you tried carrying her in a sling for a while? During REM sleep, babies can easily wake up, but since you said she can sleep in a sling, could you try carrying her about as you do something around the house, and when her eyes stop fluttering (going into deep NREM sleep) try putting her down then? My son had an awful time with sleep, and carrying him in a sling did the trick most of the time...I just had to carry him in a sling for about 15 minutes while I washed dishes or vacuumed or something, and then I put him down on his bed, still in the sling but with his face uncovered of course. darkening the room will probably help too, as you said.
Good luck!
Good luck!