Hi H..
I had something kind of similar... Similar enough that I think what we did may help. My son did NOT respond to cry it out at all ! Neither did my daughter.
But I came up with something that has helped. It is a longer process but in my opinion it is a loving method. Although every child is different and I recognize that.
I think there are two ways to go about this.....
One do this in your room first and then transition into her room with it, or to just make a BIG BIG deal about a Big girl bed in her new room. (Let her have input on paint color, decorations and maybe even let her help paint the walls, etc..
I started by getting to the point you are at.. In having the child get used to not cuddling until they are asleep. So you are farther than I was when I started.
Basically I stared by telling my child I would be sitting in the chair (placed a chair for me in the room) after saying goodnight. Progressively you scoot the chair closer and closer to the door. This can take days, or weeks. So be PATIENT. Remember you are creating a new habit and in most people that takes about 21 days. If she can and does get out of bed, quietly and without a lot of touching put her back in the bed. You can reassure her briefly that you will be in the chair. Then I would sit in the chair and not talk or make eye contact..less and less as time went on. Until eventually I said nothing after our good night routine.
Once you get to the point that she is comfortable and falls asleep with you in the doorway, you can start telling her you are leaving the room. Be prepared for resistance and you may need to move into the doorway again for awhile, but eventually my kids got used to that.
Then you can work on getting her into her room, if you didn't start there.
If you choose to take her into her room to start this, then I would actually snuggle and lay with her in the bed until she isn't scared of the new room.
My kids had issues with a new room...they were scared to be alone. We ended up with our daughter figuring out she slept much better with a dim light on. (not a night light but a lamp with a dimmer. We let her choose the new lamp and she loved that.)
Your daughter is still young so try and keep in mind that her whole life she has done bedtime in your room. So this won't be a quick process most likely. With my daughter it took several months, but in the scheme of things it was a short time.
Blessings.
M.