Trying to find an oldish sci-fi short-story, probably from the 60s-90s.

I read this when I was like 11, so the details will probably be somewhat imperfect.

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A military expedition on an alien planet ends up meeting with a small tribe of very primitive allied aliens. They are enemies with a hostile tribe, and actively in some kind of war or something with each other, but the humans, with their advanced technology, are strictly forbidden from participating. The humans are hanging around with the aliens when they're all ambushed, and a high-ranking alien is killed. As is tradition, which is apparently extremely important, a small pouch of internal organs (? or something else from the alien, can't remember exactly what) must be delivered to the top of some distant mountain.

Along the journey, most of the other members of the group are slowly killed off in accidents and skirmishes, until near the destination, only some of the humans are left. They end up deciding to complete the aliens' journey, though have to use their advanced weapons to defend themselves against the attackers in order to do so. The punishment by the human space-government was, I believe, of the capital nature.

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Any and all help would be appreciated, and I'll try to answer as many questions as possible. I looked through all the scifi anthologies I own but couldn't find anything like this in any of them. I did end up finding Private Eye, by Lewis Padgett, however, which was the other story I was hoping to locate and thinking about posting here. Really highly recommended.

Thanks!