I am one who does not like to hear a child cry themselves to sleep. I think crying can become a habit just like other habits we do over and over. A child is insecure and feels frightened when you leave them alone. Just think about where they are all day. At that age, they want to be in the room where you are as you move about. You have to work at this like anything else and it will be easier for some than others. I believe all the things you are doing are great but maybe you might try reading books and then singing a favorite song before putting your daughter in bed. We leave a sippy cup of water in the bed plus soft baby wash cloths that he likes to hold close to his face. In fact, to make the transition from rocking chair into bed when he was as young as yours, I would put several wash cloths on the faces of the stuffed animals in his bed. He would love to take them all off and sometimes play with them while I walked out of the room. He never knew when I left and would lay down and go to sleep in a few minutes. I didn't announce I was leaving until he got older and could understand me more.
So, though some will think this an odd thing to do, it worked for my grandchild. It was when he saw me leaving was the nightmare, but when he had something to occupy himself while I diddled in the room for a few short minutes and was all calm, I would just slip out without him looking and he never made a fuss. In other words, I made bedtime fun for a few minutes when I put him down. After time, they get use to being in the bed alone without knowing they are. When he got older, I was able to talk to him about me being outside the door. In fact, I tell him, that I needed to go now and clean the kitchen and he was fine with that for some reason. He is now 2 and half but the best thing to put to bed there is. So, don't give up and work on it for it will soon become an enjoyable time of day. You will find something that your little one will like to do when you first put her down and it will calm her so she can get to sleep faster. Hope this helps you. And, we read all the books but this is what worked for us.