I'm under the impression that the OG chrome toaster centurions from Razor were supposed to be human constructed models, from that generation - they would have been the advanced production versions of the oversized prototype battle robot frame from Caprica. With martial, regal styling to denote them as formally part of a (human controlled) Cylon armed forces.
Likewise, the original "pie plate" basestars seem like they were the original human designed Cylon carrier ships. The tri-star basestar we saw take on Osiris in Blood & Chrome is likely one of the first Cylon-designed ships. Likewise, the centurions seen in these episodes are the first post-toaster centurion models. They drop the pretense of serving human sensibilities and human vanity.
As to just what kind of mind is in these things, it's possible that they're copies of human mindstates, just mass produced. It was almost insinuated in Caprica. The original Graystone industries Cylon "products", both civilian and military models, were possibly stamped out by copying a few master AI chips that had human derived personalities in them. Therefore, while they were never actually real people, all the Cylons fighting in the war have human like intelligence and perhaps their own personal projection of reality. How they see themselves.
The business about feeling pain could be an inevitable side effect of the kind of AIs they are. Perhaps the minds, based on human minds, suffer from virtual neural connections to the components of the robot bodies.
As for wanting to be organic / human, remember that what the Cylons want freedom from is oppression and being used as disposable people. The First Cylon herself wanted to be human again and didn't see the joy in remaining an iron plated robot. It hasn't been revealed just what connection she has, if any, to the rebellion. Could it be that the Cylons, before the arrival of the Five and the manipulation of Cavil, wished to find some form of hybrid form that allowed them to feel some form of humanity while preserving their mechanical advantages?