If I am understanding the correctly, all of the information in the BTC programming is needed in order for the block chain to properly work right. So I am guessing in order for you to do that, you would have to rewrite the complete block chain from the start so it all lines up. Am I on the right track with my thinking?
No, "rewriting" the blockchain will not enable you to forge a signature. You either have to break ECDSA (or the specific curve used for bitcoin) or get the private key in question. Also not every single line of code within bitcoin core is needed for the protocoll to work. A large portion is the wallet part that is not required.
Rewriting the blockchain is impossible for anything but the most recent blocks, and rewriting those would need over 50% of the computational power of the entire network. Each block in the blockchain contains a hash of the previous block in its header. If you attempt to change anything in the previous block its hash changes, and the next block needs to store that changed hash in its header. All Bitcoin nodes store a copy of the blockchain containing those hashes, and if you attempted changing an old block they would refuse to accept it as valid because its hash wouldn't match theirs.