Fascinating discussion. There are two hints or a then-acceptance of reincarnation in what is currently in the Bible. I don’t have my reference handy but here they are:
1. When Jesus healed the man who had been born blind, his disciples asked if he had been born blind due to his parents’ sins, or his sins. Jesus answered that neither, it was to give glory to God. SO who could the man have been born blind due to his own sins if he had not had a previous life?
2. At one point Jesus asked his disciples who people thought he had been, and he mentioned two ancient prophets. I am very far from a Bible student so can’t find that part. The point is how could he have been, or thought to have been, a prophet from the past, without reincarnating?
The first one is John 9:1, if I remember correctly.