If I had $4000 to spend for a bike to do what you described, I would probably buy a CX bike and a road bike. There are a few CX bikes which have the braze-ons and eyelets to do light touring, but they are mostly at the lower end of the price spectrum and not made of titanium.

Take a look at something like the Specialized Tricross or Kona Jake. Consider whether or not you really need to spend your whole budget.