First: upvoted.

On this descriptive conception of laws, the laws do not exist independently in some transcendent realm. They are not prior to the distribution of matter and energy. The laws are just descriptions of salient patterns in that distribution.

I'd also like to point out the flip side of the coin: by the same arguments, it doesn't make sense to talk about matter and energy separate from how it behaves - matter isn't some primordial grey blob, which, by its inaction, forces laws to be separate objects. What we'd call "matter" and "physical law" don't have to exist independently just because we have two words for them.

Note that whether things are separate or not is pretty map-level, but I think the above is necessitated if we accept the foundation of your post.

If the fundamental laws of physics are already lording it over all matter, there is no room for another locus of authority. However, the argument fizzles [...] if we regard laws as descriptive.

I'm confused why you would argue that physical law can't be some separate thing, "lording it over all matter," but still leave room in your picture for a really existing, similarly separate "locus of authority."

Specifically, there is no reason to declare one of these methods of compression to be more real than another. What would this even mean?

I think you're taking the lack of an immediate and obvious answer to a rhetorical question as more of an argument than it actually is. The satirical extreme being, of course, "I can't think of any counterexamples to P, therefore P." Would you like me to brainstorm you up a list of ways to compare descriptions of reality? (serious question, not rhetorical - I just don't want to spend the time if you don't need me to) It would begin "objects described by laws of physics have been observed to disobey laws of economics, but not vice versa."