The only problem I have with nomological is that nobody knows what it means except philosophers and crossword puzzle enthusiasts.
True, but if a word says exactly what you mean, then doesn't that qualify it for use of that term?
Apparently you do not have a problem with the word superconductor or superfluid, or even supersymmetry. Supernatural following this use of the word should have a well defined meaning in physics. If super... means something different in philosophy, then perhaps they will have to understand a new definition. In current physics usage, super implies minimal friction, etc. So I do not understand how the philosophers reversed the meaning and usage of super... Perhaps that is your own meaning and not that of all philosophy.
The term 'super' has a number of meanings. The meaning of the term when compounded with another word forms a new word that itself is defined by that words' own specific meaning. I think it is incorrect to say that we define the meaning of a compound word (in this case, 'super' and 'natural') without looking at how that word is most often used. For example, rather than 'super' meaning 'extreme' (e.g., extreme conductor, i.e., superconductor), the term 'super' can mean 'beyond' or 'outside the bounds of' or 'transcend' (e.g., supernatural, supersonic).
In terms of the exact meaning of supernatural, it is very murky in its exact meaning. It can mean something that is apparently beyond our understanding of the laws of nature (e.g., spooky action at a distance), but it's usage in science, I don't think this is how the word supernatural is used. Otherwise, whenever we encountered a new phenomena that wasn't in line with current explanations, we would be reading how amazed scientists are at the supernatural behavior that they observed. Obviously, this wouldn't ever be said by any reputable science organization. The only hypothetical situation that I can imagine the term 'supernatural' being used in science is if scientists came to the conclusion that nature behaves erratic without any natural explanation. That is, the only explanation is one that violates natural principles (e.g., random walks, least action, least time, conservation laws, etc). The only explanation left is a supernatural one.
This is why I say to avoid the term supernatural even with what you are proposing. It gives a misleading indication that you are proposing genuine violations to natural principles, but if anything, I think you are affirming natural principles - just in an unorthodox manner.
You are perhaps bothered because the word supernatural has a definite history. It implies other worlds may exist which can support intelligent life and perhaps even gods.
Not really. I am bothered by the concept that the world behaves unnaturally at its deepest level. This proposes an ad hoc world from which all of our rationality somehow emerges. It would seem to me that an unnatural underpinning to the world would mean no such thing as natural phenomena being observed. On the other hand, a nomological world could produce natural phenomena, even though the nomological superstructure to the world is not visible to us.
So my use of the word supernatural is consistent with both previous use of super in physics and with all the implications of that word throughout history. I just think it will all be explainable with physics some day.
Physics will probably never call an explainable phenomena by the title 'supernatural'. It goes against the grain of what we mean by the term 'natural'. If the term natural is to have any meaning at all, then it must mean that which we can explain using our physical notions of conservation, symmetry, action, etc. If we can't, then it's supernatural, in which case we can't explain it using physics.