The timestream notion is a bit out there, but with quantum phenomena, one should never say never. It does seem very plausible that NSA would have a Quantum computer that has achieved Quantum supremacy. Google or IBM will have one in the next year or two, and as you say, they would try to stay 20 years ahead in this area.
CIA would probably NOT have a Quantum computer, since codebreaking is not really their specialty. That might be the determining factor that enables Q and the gang to stay one step ahead of the clowns. If their quantum computer can cut through conventional crypto like a knife through butter all of the communications of all clowns/cabal/stooges can be easily compromised.
The quantum angle might also apply to your timestream notion. A less exotic interpretation might be that they have a massive multi-agent computer simulation of the US public. It enables them to run different disclosure scenarios, and identify potential problems and tripwires in their planning.