Did anyone sleep train a baby who needed a dummy to get to sleep? What happened? How did it work?

My LO needs her dummy to get to sleep. Its a miracle device in that when she is really tired it only takes one suck for her eyes to close! At nap time, she fights that dummy, pushing it away with her tongue, crying..... but as soon as she takes that first, reluctant suck - bam! Asleep!

But I also think that the dummy is causing our short nap problem because when she wakes from her first full sleep cycle she needs her dummy to fall back to sleep. Then, because she is so sleepy, her jaw slackens after a few sucks, the dummy falls out and she wakes slightly - cue crying. I just got a two hour morning nap out of her by sitting outside the nursery door with the monitor and reinserting the dummy every time it fell out (approx every 10 mins). She had her usual half hour stretch, followed by an hour of this absurdity, before she drifted off into another half hour stretch and didn't fuss when she lost the dummy.

Im pretty sure that CIO will be for us when she is old enough. If she could soothe herself back to sleep she would be an epic sleeper. But what do I do about her dummy? Let her start the nap with it but if she loses it she loses it? Or should I remove the dummy entirely? If so, am I doing more harm than good using it as a prop now?

Its interesting to note that she doesn't need her dummy through the night. She has it at the start of approx half of all nights and does need it reinserting a few times at first but once she is asleep for the night, she spits it out and doesn't need it, even after her night feeds.