Lots of great suggestions, most especially the ideas regarding offering both options (keep both crib and bed up) and using a side rail.
For what it's worth, my own son is the same age and I have seen the same sort of indecision and vacillating with him as you have described with your daughter. While I believe in offering two positive choices whenever possible, I've discovered that sometimes HE doesn't know what he wants, and so he will go back and forth between choices, becoming even more unsure as he goes. I've since decided that, while it feels good for us to offer him choices, if I see that he's stuck, I make a decision quickly for him. There are days that his independence surges forth and he can step with confidence into his own choice, and there are other times that he really needs the security of relying on me to make a good decision for him. This may not be exactly what's happening in your house, but it's just another idea for the parenting toolbox, so to speak. You might even set the tone with something that acknowledges where she's at: "We're going to read your stories in your big girl bed, and then if you like, you may sleep in your crib" and see where it goes. She might chose not to sleep in the crib, or might change her mind later, but it's also okay to make the decision about where she's to sleep. That's what you've done in the past.
The other piece of it is that offering toddlers and preschooler such *big* decisions at the end of the day can be hard for them. They're usually tired, or if they try to avoid the separation of sleeping, this 'choice' can become a vehicle for continuing to engage with adults. And this is why you might choose to reevaluate how/if having a choice is helping your daughter rest well or just exacerbating the problem.
We are currently co-sleeping and offering our son a (very cushy) tent on the floor of our room. (His room is on a different floor and the step are steep, hence our decision to keep him safe and close with us.) Some nights he wants to sleep in the tent; other nights he starts his bedtime routine in the tent then proclaims he wants to "sleep on the bed" with us. After this point, no matter what happens or if he changes his mind again, he stays on the bed. The point being that we are not spending our evening going back and forth; instead,he knows that mama is in charge, making a good choice for him, and he sleeps just fine. All that to say, different circumstances, but I know where you're coming from!