The gravitational wave background you linked is extremely weak, it took decades of measurements of pulsar timing and complex signal processing to even see hints of it. In general, the gravitational force is so much weaker than the other forces that it can be ignored except on very large scales. So I’m not seeing how a rogue gravitational wave would produce sufficient energy density for creating matter via pair production or some other mechanism. You would need extremely large amplitude gravitational waves, which would require some even more energetic mechanism for generating them. Maybe this is something you can work into your model?
I was most impressed by a single fact of physics that all energy in ordinary matter is equal to the negative potential gravitational energy of that matter.
I’m not sure what you mean by this, could you point me to a reference where you saw this statement?
I will come back here to answer your questions one at a time … )