Like caethan said, sacrificing seems to be capable of "paying" for about one animal per day, regardless of size. If you're hunting actively you can regulate the flow somewhat by stopping when you have enough, but if you use traps you have no control over when animals enter them (and they tend to arrive in groups as well).
There are some things I dislike about the changed sacrificial system:
1. The price seems to be one animal = 1 demerit point (and you seem to get those for chopping trees as well). It would make a lot more sense if bigger animals had a higher "cost", if for no other reason than to avoid punishing a small game hunting life style unfairly.
2. A daily sacrificial chore that is also the maximum sacrifice that has any effect doesn't seem right to me. As far as I know, most cultures performed sacrifices either in anticipation of something (before a sea voyage, etc.), or in gratitude to something (killing an elk, winning over an enemy, a good harvest, etc., or to ward off bad luck (diseases, etc., especially when something was going around).
3. A common sacrificial pool for all sacrifices doesn't seem right either. The spirits of the water ought not to care of whether you've sacrifices to the spirits of the forest and vice versa.
Note that there are rituals my character doesn't know yet, so there may be dedicated sacrificial rituals that are still unknown. However, the spirit of the forest could be invoked with the general sacrificial ritual, and my character was hit with unsteadiness (i.e. the daily sacrifice had already been done in the morning, so additional ones were useless), for it, but the ritual still worked.
Also note that I have no knowledge of Finnish Iron Age spirit relations, so I can be barking up the wrong tree.