I had the same problem with all five of my children (or maybe it was with me? Hmm...) I refused to let them cry it out. I was lucky enough to be a SAHM, so the most pressing things I "had to get done" were taking care of the other children, taking them to school, etc. But we managed. Have you tried letting her fall asleep with you in your bed (taking care that she can't fall out, pillow surrounds, bed rails, or putting your mattress right on the floor) then creeping out after she falls asleep? this worked with all of mine. Still takes a long time to get them down, but you get some alone time. That is if you don't fall asleep yourself next to your little bundle of sweet smelling warmth. Which isn't the worst thing for a new mom. My three year old and two year old still need someone in the room to fall asleep. I am sure other parents would scream, but i let my kids fall asleep to quiet childrens television when they are old enough to be interested. a channel like noggin with no commercials, or a low energy kids DVD. Gives them something to focus on, so they don't realize you are trying to put them down. Another thing we used was a baby bottle of water. My kids all nursed to sleep, so giving them something to suck on that wouldn't harm their teeth somehow soothed them into sleepiness. You can start with watered down breast milk (or formula or juice if you don't want to pump), and slowly add more water every day until they don't realize it has become water. It's not great for her teeth but if it only takes you a week or two to get her on full water it might be worth it. Helps if you make it warm like breastmilk. Also, create a bedtime, naptime routine. Put crib in darkest area of house, play a soft CD, the same everytime. When you change diaper right before sleep, spend an extra few minutes rubbing some baby lotion into her arms, legs, torso in soft, downward motions. Rock her, sing to her, or lay her in crib if she'll let you, till she's mostly asleep, (have crib rail down before you do this! hard to do with one arm) then gently move her to crib. If it's the crib that freaks her out (it did mine, they woke up during every transfer) try putting the crib mattress on the floor so she can't get hurt (assuming the nursery is childproofed) and sitting on it next to her while she listens to a soft CD and goes to sleep. Then when she is asleep you sneak off and get to work. Leave a baby monitor on so you can hear when she gets up if the room is not childproofed. The transistion to actually sleeping in a crib will come after she gets used to waking up alone, and staying asleep not on your shoulder. Another thing- will she fall asleep in a stroller? I frequently took my kids for a walk, buckled up in the stroller till they fell asleep, then parked them near a stereo for cover noise so I could do my thing and see when they woke up, but they were buckled safely in. On rainy days we strolled inside the house which takes longer :)
Most of all, don't listen to people if they are telling you to do something that goes against every bone in your body. Letting my children cry themselves to sleep was never an option for me. Not that I didn't try. I am not a sappy mushy parent, I believe in raising self sufficient children, independent thinkers. I insist my children show all adults and people respect, they are well behaved, well disciplined kids. Maybe they are that way because they didn't cry to sleep??? But I also believe as a parent you do what you feel strongly about, and that was one for me. The few times I've been talked into doing something with my kids because other people thought it was the right idea, I regret each of them to this day. Especially crying it out. since i ended up doing it how it worked for us in the long run, now I look back and wonder why I ever put them through it in the first place. I knew it was wrong for us then. I've learned now to trust the mother bear voice inside. Follow your instincts and you'll be doing what is best for your daughter. All children are different. The strong will she's showing now is the same strength you want her to have later to stand up to peer pressure and those nasty teenage boys! Hard to remember, I know, I have two strong daughters. But now they are older it is the not-so-strong willed one I worry most about, not the other two. Good luck...and enjoy your daughter.