You could try a setup like this. Some things to note - First, as you can see from the graph, Bump Nodes facilitate Normal inputs, and Displacement Nodes are used for Displacement. Displacement doesn't have quite the effect in EEVEE as it does in cycles, but it still does has some effect (especially with Ambient Occlusion turned on).
On the topic of Normals, the contrast of generated textures (Such as a Noise Texture), is far too high to be able to plug directly into a Bump Map at full strength and still have it look "natural". As you can see in the graph, I mixed the result of a Noise Texture .996% with pure white. and I still had to reduce the strength of both the Bump Node and the Displacement, otherwise it still looked too strong.
Although I know it breaks the rule of Metallics/Dialectrics, I found the materials benefited from a slight increase in the metallic values, to work in conjunction with the roughness to make the reflections (or sheen) look a bit more realistic given your lighting setup.
Lastly, as you can see, I mixed some Ambient Occlusion "shadows" with the base color, which allows for some extra perception of detail while keeping the Normal Strength on the subtle side.
To save you the trouble of setting up all the nodes again (as I have already done it), I will post your .blend with my modifications, so you can see the results without too much effort, and can then decide whether something like this works for you.
File is here -
As a final note - I know the example I used is in EEVEE, but it works just as well in Cycles.