If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Notes for future OT posters:
1. Please add the 'open_thread' tag.
2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)
3. Open Threads should be posted in Discussion, and not Main.
4. Open Threads should start on Monday, and end on Sunday.
Again, this is very different from the situation with entropy. I think you're confusing two meanings of the word 'model'. It's one thing to have an incomplete description of the physics of the system (for instance, lacking nuclear forces, as you describe). It's another to lack knowledge about the internal microstates of the system, even if all relevant physics are known. (In the statistics view, these two meanings are analogous to the 'model' and the 'parameters', respectively). Entropy measures the uncertainty in the distribution of the parameters. It measures something about our information about the system. The most vivid demonstration of this is that entropy changes the more you know about the parameters (microstates) of the system. In the limit of perfect microstate knowledge, the system has zero entropy and is at absolute zero. But energy (relative to ground state) doesn't change no matter how much information you gain about a system's internal microstates.
I understand what you are saying, but I am not convinced that there is a big difference.
How would you change this uncertainty without disturbing the system?
How would you gain this information without disturbing the system (and hence changing its energy)?
EDIT: see also my reply to spxtr.