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Bet $ you could hike a good trail much faster than bushwacking a shorter route. I know it takes more time and effort to hack thru the woods. No thanks. Beside what if there is an obstacle, creek, cliff, etc. you encounter? Then what? No, trail of a couple miles isn't too bad. Of course the terrain is the deciding factor but I see bushwacking as not a poke in the woods but rather a brush filled mess and not knowing whats coming next 50ft in front of you. As for hunters, well if an animals down they are second fiddle. We responsible to recover animal to best ability.
Most likely you will blast out the herd once you get yours on the ground. Then you have the quartering out and loading packs. This takes time and if its morning, you're starting your pack out late am or noon. If you get your elk down in the late afternoon, you're packing out in the dark. Either way, any hunter you run into aren't likely to find any elk in the area you've already scored in. My Good Luck, I hope you get to find out!
I just hope you get the chance to have to make the decision!