Crying behind the door and not coming out is a step toward her independantly going to bed. It’s hard and you’ll feel like crap but ignoring her will mean she gets bored and repeating the back to bed routing will show her you are the boss not her.
Just keep it up mate however hard it is and remember – no sleep doing this is better than no sleep and not making progress.
She is too young to undertand reasoning properly so explaining gets you no where. Keep on with the routing, bath, drink, bed and putting her backinwhen she wakes.
You WILL get there I promise. My sister is a child pshycologist – that’s where I got this from. It REALLY works.