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I have never done that event, but I've done numerous triathlon and running events, including an Ironman. I was also an event coordinator and director for several years. Be sure to check whatever organization is providing the insurance for the event. Usually, its done through a national organization that all participants are required to join. Their rules may state no carrying during events as part of being a member. While not 30.06 so it wouldn't be "illegal", they could bar you from any future events should they find out.

I also think concealment will be a major issue given that you are wet while running, climbing, crawling, etc. Again, while printing or accidentally showing the weapon may not be illegal, you will be in close quarters. If someone complains to the event director that there's a man with a gun they get you kicked out of the above organization. Additionally, if the director learns you are carrying and deems it "unsafe", they can likely remove you from the course according to the terms you agreed to when registering. I've always seen some sort of "do what I say or I can remove you" clause in the terms.

As someone else suggested, you may want to consider leaving the weapon in the car during the event. Once you are done "competing", slip off to your car, rearm, return to the after party and carry on.

p.s. Have fun! I've always thought that'd be a fun event to do!