I think the bit about the fresh kill doesn't actually mean that the thing you sacrifice has to be from a freshly killed animal, at least not the way things are coded right now. I think what it means is "if you don't perform a sacrifice soon after killing an animal, the gods will get mad at you."
I think that right now there are different buckets of items: [dried fish, dried meat, smoked fish, smoked meat, roasted fish, roasted meat, raw meat] are in one bucket, [raw fish] is in another bucket, and [silver] is in a third bucket. When you sacrifice an item, it looks up which bucket the item is in and adjusts your relationship with the spirits according to the rules for that bucket.
Separately, there are different buckets of actions: [fishing] is in one bucket, doing it lowers your relationship with the water spirits. [killing big animals, letting big animal carcasses rot in your traps, just taking the skins and not using the meat, excess trapping, excess felling trees] are conjectured to be in another bucket. doing those things lowers your relationship with the forest spirits.
Probably the rituals where you ask for something also affect your relationship with the spirits -- before we had spells, anyway, asking too much made them angry. so probably some more buckets for rituals where they adjust your relationship up or down based on a bunch of factors.
Whenever you do a thing, it figures out whether your relatinoship with the spirit should go up or down by checking what bucket the thing you've done is in.
tl;dr:
So what I was initially arguing was that dried/smoked/cooked fish does not belong in the same bucket as meat, but in the water bucket. You guys have convinced me that actually dried/smoked/cooked food probably doesn't belong in either the forest spirit bucket or the water spirit bucket, but maybe in some generic third bucket.