and regarding to blood manipulation in the atonement ritual that was only a religious ritual that served as a single part in the whole complex of "sin-covering"-and "forgiving".
The achieved atonement was not meant to be "legally" payment for sins towards god as JW see it. - "you kill the animal and thats it, the payment for the sin" No, It was rather a religious ritual to come closer to god together with priest, family and friends during a festival, a holiday meal (like at shabbat) because sacrifice in hebrew means since always not a "payment" or "ransom" but it means a "gift" for god that, to come close to him, atonement doesnt turn around a juristical ransom but about loving relationship with god.
Therefore the bloody community sacrifives were ALONE not enough to shop repentance for unwillingly sins. But only together with forgivness and reversion and consious repentance it was seen as effecitve way of jewish Teshuva = repentance
Note: Bloody sacrifice were only a part of teshuva, without reversion actually not effecitve.