We must either say that the rules are the necessary entity or matter/energy is ...
So you are accepting that matter/energy or their governing rules may be the the necessary entity (if there even is one). Well those things clearly lie within the sphere of the physical world, not outside it, they are clearly amenable to standard scientific observations. So you seem to be arguing against yourself as elsewhere you seemed to imply that a necessary entity must exists entirely outwith the physical world, not interact with the physical world and therefore not be amenable to standard scientific observation.
... or look elsewhere.
Indeed - but the place to look would be within the sphere of the physical world involving entities that are part of that physical world and interact with other entities (contingent ones) within that physical world.
An alternative approach would be to consider that there is no necessary entity and that all entities inter-relate in a mutually contingent manner.
Of the two, the rules of nature with an existence independent of matter energy is to my mind a better candidate for necessary entity than matter/energy/rules or matter/energy, since matter/energy can be actualised.
Depends on what you mean by the rules of nature - I think this kind of implies life, in which case I'd close you down straight away as it is pretty clear that life doesn't need to exist for the universe to exist so cannot be a necessary entity. Fundamental principles of physics - well perhaps.