Another salty dog here(USS Independence CV-62). I've been riding Sullivan on my cross bike for years. The fireroad is very CX friendly but I have to warn you that you will be getting a lot of stares from the local mtb'ers
. And yes, the steeper the trail the better. CX bikes are just perfect for climbing. If you are still shopping for a CX bike I recommend getting a nice steel frame. It helps muting the trail roughness.