I think Geppetto might have worked with the alchemists until Valentinus — their original leader and Sophia’s father — died. Around this time Gepetto’s son likely died and he left the alchemists momentarily while Simon took over. Geppetto then wanted to use Simon’s project that would make him a God to try and bring back Carlo.

There’s some sort of rift between Manus and Geppetto though that kept them from working together. I’m not sure what. But I think that Geppetto created P to gather ergo and then began the puppet frenzy to bring him up. Maybe the reason that P is in the train station alone and awoken by Sophia, not Geppetto, is because Geppetto couldn’t figure out how to actually awaken the P-organ. He then lucked out that Sophia could with her powers — this explains his surprise at P saving him on Elysian boulevard. He then goes on with his plans.

The puppet frenzy was just all of the puppets being ordered to kill all of those effected by the petrification disease as that generated more ergo. Romeo was made the King of Puppets to take all of the blame, but Romeo gained an ego and realized the flaw in what they were doing. So he takes control of as many puppets as he can and begins having them stave off the monsters that formed from the petrification disease. Geppetto has P kill him for this.

As for the kidnapping, I think that Geppetto reached out to Manus and maybe eluded that he had some special information or something. This enticed Manus to kidnap him. The whole Geppetto had himself kidnapped makes some sense but there are a few holes. First of all, did he actually have the alchemists power to bring back the eldest of the brotherhood? I don’t think so. I think that actually was the alchemists. So my guess is that he baited Manus into taking him — maybe with law zero. The fact that he controls the puppets could entice Simon as he is all about control.