To emphasize god rays, best to use Single Bounce. Also best to keep absorption (which is what darkens everything else, by absorbing light) at something like 254, 254, 254 (can't use 255 as that would mean zero absorption, which would mean no volumetric effect at all).
For getting the two separately, you could try the Components multipass with everything checked there (Diffuse, Indirect Diffuse etc.) and a Volumetrics pass, and then combine those in post (you could instead individually add passes for Direct, Indirect, Reflection, etc. but that would be more work, and I think the Component pass would probably get you what you need with less to recombine in post).