You are asking a lot for one bike. For the crushed stone trails, you need a 32 mm tire at a minimum, but 35 mm or 38 mm would be better. The problem is that these will slow you down in your triathlon. For the triathlon, you really want 23mm tires and aero bars. You would not want the flat bars of a fitness bike for a triathlon.
Your best bet might be a cyclocross bike with 35 mm tires, a second set of wheels with 23 mm tires, and a set of clip-on aero bars. Check out the Felt F1X or the Trek XO1.
The Trek Pilot or Specialized Roubaix might be able to take a 32 mm tire. I am not sure about that, but you could check with the dealer. If they do, they might also be good options. In that case, you would want a second set of wheels with 32 mm tires for the crushed stone trails, and use the 23 mm tires and clip-on aero bars for the triathlons.