that's a nice theory you have there, jump starting his heart with his devil. Unfortunately there's no evidence to support that claim.
I never suggested Monet could restart her own heart, my guess is in the second paragraph, she put herself into a slumber which puts her in state of suspended animation having the effect to slow or stop her biological functions so that her physiological capabilities are preserved, thus helping the wound to coagulate while conserving herself.
Surprise reveal or not, Monet's purpose is fundamental to reach the One Piece without her there is no Pirate King. Her knowledge of the Moons and the most chaotic sea in the One Piece world, the new world, is essential.
Doflamingo lied to her, deceived her, manipulated her and used her loyalty against her to keep her locked in his cage. In short, Luffy is her savior. As for her sister Sugar, she's of no importance at this point, they never mentioned each others name or had any interaction in the story.
By the way, there are three strong parallels with Monet, first Monet as a bird and Doflamingo's birdcage. Second, Monet the loyal subordinate who allegedly died and the reappearance of another trustworthy follower who was supposed to have been killed as well, the Hyena Bellamy. Then the third, the sisters Monet and Sugar in comparison to the two brothers, Doflamingo and Rosinante.
It's fine, i believe Monet is alive and she will join the crew.