C.A.
The other 2 suggestions are fantastic. I also have another thing to try. Have you ever considered taking your child to a chiropractor for a check up? Babies, toddlers, and children of all ages can sometimes get something out of place by the birth process, falling or just playing rough. It is call a subluxation. This can affect how they sleep, cause bed wetting, mood swings, increased ear infections, signs of colic, unusual behavior like banging objects against their head or banging their head against a wall. My nephew had a subluxation in his neck that was most likely caused at birth. He had trouble sleeping and was really a fussy baby. After a few months we noticed that he wouldn't turn his head all the way to one side and he was developing a flat spot on the side of his head because that was the only side where he could sleep. Sure enough after his first adjustment he slept through the night for the first time! His movement got better and so did his demeanor. Later when he was a toddler/ preschool age he would just go crazy at bed time. He wouldn't sleep in his bed, woke up frequently in the night, only wanted to sleep with mom or dad either in their bed or on the couch. Sure enough he was out of alignment again so they got him adjusted a few more times again and he was sleeping back in his own bed. A couple of office visits just might be worth it to make sure nothing is wrong with her physically.
If everything checks out then it is time for some tough love. The transitioning method with a nightly routine schedule is the way to go. It will be nerve wracking at first but hey what's another week of screaming if it means future easy bedtimes? One big thing to remember is that once you do your bath/ book, tuck in bed (or whatever routine works for you) then you do not give her any eye contact or talk to her at all after that. If you sit in her room make sure the lights or off (maybe just a soft night light glowing) and you don't look at her or say anything. If she gets up just quietly pick her up and put her back to bed and go sit in your spot. If she just screams then let her but don't tell her to be quiet. Talking and giving her eye contact gives her your attention which is what she wants. You might have to do this over and over and it may take a few hours so get someone to help watch the baby. You should see some signs of improvement by after 2 days. In another words she might not get up as much. Within a week (sometimes as little as 3 to 4 days) you should be able to transition yourself more and more out of the room without her getting too upset. Remember children learn by repetition. If every time she gets up out of bed and you put her back will help establish this learning.
Now some notes for YOU. Transitioning will be hard and you may feel terrible about doing this. It might make you cry or doubt yourself that you are not doing the right thing. You might feel guilty or want to cave and say "Maybe we will start tomorrow." Don't give in! You can do this. I recommend keeping a ton of tissues in your pocket, keep a pillow to cry into close by and invest in some ear plugs. The end result of your little one being excited and happy about going to bed will far outweigh your guilty feelings now. Trust me I know! My daughter is almost 6 now and every night our bedtime routine is such a pleasure. I love seeing how at peace my daughter is every night. She goes to bed happy and she wakes up just so relaxed and joyful. We have had this for years now and I love it! So remember that 1 week of torment will feel like nothing once you see the results!