I cited a lot of verses to support my position, so if you think that they would have disagreed, then please explain why.
The Bible does not say anything about efficiency being relevant or about the Mosaic Law being inefficient, and if you think that this was evidenced by Scripture, then please cite it. The Mosaic straightforwardly did was it was given to do and did not do what it was not given to do. Everything taught in the NT is based on and in accordance with what was taught in the NT, so there is nothing that was improved. You can't have a better set of instructions for how to walk in God's ways without following a better God with better ways.
In Matthew 23:23, Jesus said that faith is one of the weightier matters of the Law, so following it is about expressing our faith in God to guide us in how to rightly live. Living by faith is always associated with living in obedience to God's will, such as with the examples of saving faith listed in Hebrews 11, whereas disobedience to God's instructions is referred to as breaking faith, such as in Numbers 5:6. In James 2:17-18, he said that faith without works is dead and that he would show his faith by his works, so obedience to God's Law is what faith looks like, which is why Paul said in Romans 2:13 that it is only the doers of the Law who will be justified and not the hearers. Trusting God through refusing to follow His instructions is not a concept that is found anywhere in the Bible.
There are certainly night and day differences between how health it is to eat clean and unclean animals and there are an incredible amount of parasites and diseases that have been transferred to humans through eating unclean animals, so perhaps health had something to do with it. However, in 1 Peter 1:16, we are told to have a holy conduct for God is holy, which is a quote from Leviticus where God was giving instructions for how to have a holy conduct, which includes Leviticus 11:44-45, so God associated His holiness with refraining from eating unclean animals and following those instructions is about testifying to the holiness of our God. So there is much more to it than being survival information for starting up a new settlement.