I believe that the ECC/NSA thread you referenced did eventually nail down every parameter used to create secp256k1 and answers most if not all concerns.
Yes, There is a python script that produces every parameter for secp256k1 from first principles, except the generator and both myself and D. J. Bernstein have given the proof that in-advance choice of the generator is harmless outside of restricted conditions that aren't relevant to normal Bitcoin usage.