So I'm guessing that Richard Parker isn't Peter's dad, but an older clone of himslef.
I do think the CIA bits are implanted memories. I do think he's a clone.
But I think he's a clone of Richard Parker.
The Carnage Prototype was a mesh of Peter Parker's DNA and Richard Parker's DNA. The reason I feel that it remained so unstable is because Human DNA and Oz/Spider/Human DNA doesn't mix so well. This meant that Carnage was trying to imprint the DNA of others into himself to stabilize himself.
Once they figured out how to isolate Richard Parker's DNA in the monster, they were able to create a human clone of him.My guess is that Miles Warren works with Cassandra Webb and has been provoking Aunt May to think about her brother-in-law and all of the aspects of his life she knew about, so Webb could read those thoughts with her telepathy, so that the fake memory they developed for Richard would be more realistic.
With the R. Parker DNA pulled out, it would be easier to analyze the genetic properties of OZ and unlock the formula for cloning Peter Parker. The first attempt would probably incorrectly balance the human and Spider genetics, and create Tarantula. the second might be closer, but require them to put him in an exoskeletal suit, if he wasn't created with a complete skeletal structure, creating Scorpion (using a tail that acts in the same way as Doc Ock's tentacles do, i might add). Then they would create their first successful mostly-human form, whose skin starts to deteriorate, and then his brain as well, leaving him more than a little insane and unbalanced. Perhaps he's living over all of the traumatic experiences in his life, making him desperately want to save MJ. Spider-Woman, would be the last and most successful clone.
Using the remnants of DNA in the original Carnage subject, the Reily team, using the mind of the original Richard Parker, as well as Doc Ock, go at focusing the DNA eating goo into holding onto the life Force of Gwen Stacy. Perhaps they think that if they can stabilize the creature as Gwen, then they could take Gwen's DNA and clone her. She escapes at this point, convinced that she is gwen, but still being Carnage.
Thats my guess