Hi Sara,
Your essay presents your case very nicely. I agree that "informational efficacy" identifies something unique about living things, that certainly deserves more thought. But I tend to imagine this as resulting from the evolution of life, rather than as the defining feature of the process.
You distinguish above between "trivial" and "non-trivial" kinds of self-replication, where the latter involves "explicit programming". More typically, I think biologists (going back to Darwin) say that what makes biological replication non-trivial is that it produces inheritable variations, which subjects the process to natural selection. What you emphasize - the informational control over the chemistry - is made possible by this selective process.
The primitive self-replicating systems that eventually gave rise to life would not yet have shown this distinction between the programming and the chemistry it controls. For example, if such systems were something like bags of complex molecules that catalyzed each other's construction, all the molecules would have been part of the control-mechanism. I'm not clear through what stages the control-function might have become segregated into a specialized sub-system, eventually leading to the actual encoding of programmatic instructions in stable DNA molecules, with mechanisms for translating that information out into the protein-chemistry. But I can imagine many reasons why this would be advantageous - supporting a remarkably accurate/reliable replication process while including mechanisms that produce and control variation.
I think you're right that this discussion is relevant to fundamental physics, though I would make the connection a little differently. I suggested at the end of my essay that there might be an evolutionary process in physics analogous to the biological process, but based on the functionality of communication rather than self-replication. Then we might think of the "laws of physics" as having a role similar to the function of DNA in biology... as a controlling information-structure that evolved to support the structure of interaction that makes things observable.
In any case, thanks for your contribution -- this definitely brings a different perspective to the question of how information works in the physical world.
Conrad