If you want to study the Old Testament, it helps to compare the Tanakh with the western translations, which is what I did in college in my various religious studies classes with an emphasis on Jewish studies. The concept of sacrifices exists in the Tanakh with the most profound one being Abraham being asked to sacrifice his son, Isacc to God, which then gets reflected back into God's sacrifice of His Son for man in the New Testament.
I measure my pastors' sermons (and have attended different churches with a range of theologies) with my religious studies as a college student. The Old Testament courses were taught by an Orthodox Jewish Rabbi with a PhD in Jewish studies. One of most interesting classes involved reading the writings of as many as 30 different perspectives on the same thing by present day and ancient Jewish scholars/rabbis. This provided an interesting perspective since different scholars stressed different Jewish sources, rabbinical writings, and other scholars in their writings.
As an example, the Jews have written on how God created the Universe from nothing. The Bible says God created the universe from nothing, but not how. One theory was God was so "huge", He simply withdrew slightly into himself to make room for the universe. The concept expresses how enormous God is and how tiny the universe is. This concept now is particularly interesting given that we now know the universe continues to expand and that there may be thousands of universes. Since it accounts for these modern discoveries and beliefs.
You have heard the joke, Christian theologians have debated how many angels can fit on the head of a pin, but the Jews have debated such concepts for thousands of years. The Jewish law is largely a product of those debates.
My studies by necessity required looking at many passages in the Talmud, and Mishnah or at least translations (which will obviously lose something, but I had no choice not speaking ancient Hebrew).
The concept of sacrifice was quite common in all Near Eastern religions. There are some interesting studies on sacrifice by Jewish Rabbis online even today. The legacy of Israel's early sacrificial system carries through in western theology and the New Testament as does the Jewish debate over it.
Jews have argued that the Talmudic Jews misunderstood passages like Leviticus 1:9. The concept of sacrifice was highly debated with some arguing the "heart" was more important than the sacrifice as Jesus says about the old woman that gives what little she has. And yet in the same story, evidence that other Jewish scholars felt that the quality of the sacrifice was important, which is why they sought out unblemished animals. The story of Cain and Abel also reflect God's response can differ.
I did not put words in your mouth, nor did I put words in God's mouth. My point is arguing one theology over another most likely misses the mark. In my opinion, a useful tool is the use of modern crowd theory to decipher God's Words in the Bible.
People all have biases, and even the "nuances" that you think you understand are influenced by your bias. You revealed some of yours with your reference to Karaite Judaism, which was included as a perspective in my Jewish studies, though not a dominant one.
In addition, our brain will influence our understanding of a passage. Karaite Judaism rejected Talmudic beliefs. Okay, but it does not make it correct.
It is better viewed as similar to Protestant beliefs compared to Catholic beliefs. Karaite Judaism believes focused on the Tanakh as all important and dismissed all previous interpretations of the Tanakh as flawed again not unlike Martin Luthor. Such rejection is common in theology, it does not make it right or wrong.
I tend to embrace crowd theory when distilling what large numbers of well-intentioned people are observing. Crowd theory argues that all of us see the same thing differently because of individual biases as you and I both have. But if you look for the common elements in all those views, those are likely to be the least biased and hence most true.
I likewise wish you well and blessing in your walk with God and encourage you not select any one theology to measure the others but look at them all is the product of human bias and the common elements among them less likely to have been influenced by bias.