Your links are irrelevant to the OP's question because Christians are human, and all humans, Christian or not, have been gifted with a conscience. So, the question isn't "Did Christians favor the abolition of legal slavery?"
The question is "Did the Christians who favored the abolition of legal slavery do so because they were moved by their conscience or by the teachings of their faith?"
Since there are more than one hundred references to slavery in the Bible. and none condemn the practice, the correct answer to the question isn't in doubt.
The answer is in the links. But I'll try to simplify it for you.
It's a combination of both. A combination of their consciences and the teachings of Jesus in the new testament.
They (the Christian abolitionist) are no different than people like myself in this modern day who chose to focus on Jesus' teachings of love for our fellow man, even if they are LGBT for example.
Luke 23: 39-43 comes to mind.
39 And one of the malefactors which were hanged railed on him, saying, If thou be Christ, save thyself and us.
40 But the other answering rebuked him, saying, Dost not thou fear God, seeing thou art in the same condemnation?
41 And we indeed justly; for we receive the due reward of our deeds: but this man hath done nothing amiss.
42 And he said unto Jesus, Lord, remember me when thou comest into thy kingdom.
43 And Jesus said unto him, Verily I say unto thee, Today shalt thou be with me in paradise.
Jesus was speaking to some criminals here. Even though they went against what the Bible teaches. Even though they broke the law. Jesus still forgave them while he was being killed, in the same manner as them. It's a powerful message when you think about it.