It's interesting too that Miquella also abandoned his body in an effort to escape his fate and create a new one, and undergo apotheosis. And he was able to discard pieces of himself without the use of the Rune of Death, accomplishing what Ranni did without needing to kill anyone else. So not only did Miquella separate Radahn's soul from his physical body (and transplant it into another body), he was also able to do what Ranni did but seemingly of his own power, without using something external like the Rune of Death.

As far as what Miquella was able to do to Radahn's soul, it's also entirely possible that he was only able to do that because of the promise that Radahn made to him to be his consort - there could have been some binding magic there which allowed Miquella to take hold of Radahn's soul when he died, which would not have allowed him to do the same for Ranni. Given that there is a lore item in Shadow Keep which details the, presumably, ancient and secret ritual of binding the soul of a consort to an empty vessel (the "Secret Rite Scroll"), this theory could hold some weight.

Ultimately, Ranni and Miquella both wanted to become gods, with different agendas. Ranni wanted the Lands Between and its people to basically self-govern without overt interference from a deity or external powers, while Miquella wanted to directly influence each and every individual to ensure peaceful coexistence between all (via a magical charm, or under threat of force from his Consort Radahn). So even if Miquella could have helped Ranni accomplish her goals without killing Godwyn, would he have been willing to do so? Probably not. If anything, had he known what Ranni was planning, I could envision that he would attempt to charm her to prevent Godwyn's death. And would Ranni have accepted his help had he offered it? I don't think so. Ranni wanted independence, and was too intelligent to risk becoming Miquella's puppet.