Just for reference, the rifle stock carry is great as long as it is secure. But, I watched a guy who was hunting bear and moose in a remote Alaskan site who used a rifle stock ammo slide similar to yours. They hiked miles up a mtn and were glassing for tgts when a big Bull Moose appeared below. They put on a long stalk up and down the rough terrain for a few hours before taking three shots that downed the moose with his 338wm rifle. At that point he had one rd left in the rifle and went to reload and found that ALL of his ammo had fallen out! Now he had one round only left and all his spare ammo is miles away in camp.
That is bad enough but in addition, his guide is armed only with a pistol (bad move in bear country) and the three shots on the moose are like ringing a dinner bell to brown bears that have learned that this means an easy meal off the gut pile. They spent several tense hours quartering and packing out what they could before dark. He survived that ooppsie but learned a major lesson. I considered this when I chose to use the loops in my vest but I first tested them for security during a week long hunt the year before and I always had another half box of 10rds in my back pack nearby.
As for who uses a fanny pack to hunt? I do, all the time. I put the items I am most likely to need in the fanny pack and carry it with the pack on my front for easy access. Range finder, para cord, knife, snake kit, hunting license, etc are all typical contents. I use it for everything from squirrel and deer to Blude Wildebeest. It is very handy. Not stylish but what the Hell? This frees space in my back pack for spare ammo, bush lunch, water, poncho if in wet climates, etc.
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Nimrod posing with his 1st African Beastie - with his camo fanny pack