My LO loved her RnP, and for the first 6 weeks, she pretty much slept in that exclusively, except for an occasional try in the crib. The thing I've found that helps my LO sleep the best is consistent naps during the day, and her swing (I only use it for naps during the day). So you may try that. Often said sleep begets sleep.
I do recommend if you are trying to get her to not sleep on you, the transition will be rough regardless, I would just start her in her crib (maybe with a sleeping wedge to elevate the mattress). Ive just started getting LO in her crib, and it's a rough transition (lots of non-feeding wake ups at night with me getting up to help her go back to sleep). So instead of having a rough transition to one thing and then the crib, just go to the crib.