Wish I could come up with a major answer, but I do think you need to lose the cot if she's climbing out. It would terrify me that she might wake in the night, and hurt herself climbing out.
Can you take the sides off, or do you have a bed ready?
I think I would make a huge deal about it, let her help make the bed, choose the toys to go on it, and make it seem a really clever thing to do, to sleep in it all night.
Then, do the usual thing of putting her down, pottering around until she settles. Gradual withdrawal etc. And, I'd do it tomorrow, rather than putting it off.
My eldest was a rubbish sleeper, and we tried everything. My youngest was a dream, but he's nearly 6 years, and has suddenly decided he'd rather read under the covers... never-ending battle.