"My family is doing a 5-day, 75 mile hike in Yellowstone later this month. If I go to a number of calorie counting websites (ie caloriesperhour.com) I find that for a 10-hour day of hiking I should be consuming 8300 calories (age 43, 230lbs)."
The average number of calories burned by a Tour de France rider is 5900, with a max of 9000. These guys are working waaaay harder than you will be on a 15 mile day. IIRC, Dr J and Co estimated they would burn up to 7000 calories/day during the Arctic 1000, but they were doing high mileage in challenging terrain. Again, IIRC, for the first week or so of the trip, they relied on body fat to provide a significant percentage of those calories and thus carried only 1.5# of food/day to supplement it, heavily weighted toward carbs to support the metabolism of body fat. If you have body fat to spare, you might want to check out the Arctic 1000 website write up on their food strategy. I suspect you could use the same approach they did during their first week on your 5 day trip and do just fine. Of one thing I am pretty certain: You won't need 8000 calories/day. I have been using that strategy for several years now on trips up to 10 days, and it has worked very well for me. I bulk up before a trip and lose the excess fat during the trip plus a pound or so occasionally, at a rate of ~1/2 pound of body fat/day, not enough to cause damage. My 2 cents.