I'll try to bring your solution back to thermodynamics terms:

The universe always has and always will obey certain invariances, and those are a redundancy in your observations, which (along with any other redundancy that could possibly be derived) is already taken into account when computing information-theoretic entropy. If you had plenty of data already to derive the invariance but just hadn't previously noticed it, that lack of logical omniscience is why the 2nd law is an inequality. Including the invariance into your future predictions isn't a net reduction in entropy. It just removes some of the slack between the exact phase-volume preserving transforms of physics and the upper bounds that a computationally bounded agent has to use.