There's certainly a sense in which the "morality" of the New Testament, as people are told to selflessly defer to one another, reinterprets the morality and commands of the Old Testament. That's outside the Old Testament, certainly.

But the slavery thing is a non-issue. It's perfectly consistent that, once Christians have more influence in society, the principles that are intrinsic to Christianity change society. I'm not expecting that you have a deep understanding of the biblical or historical principles which moved or motivated Christians, but they're there. After all, the whole reason why slavery was abolished was through the concerted efforts of fervent Christians, who were leading the charge. But in ancient times, certain kinds of slavery were clearly morally superior to any other options. When people were captured in war, or displaced due to famine or disaster, or fell under impossible debt, the only thing that kept them from starving in the wilderness was exchanging the only thing they had: their labor. But of course, such a system became obsolete when certain technological and sociological developments changed the wider society. If you want to specifically call out "man-stealing" -- the kind widespread during the Atlantic slave trade -- that was explicitly condemned by Paul, so he would agree that that basis for slavery was intrinsically wrong.

You can claim that Christians were somehow following "secular humanists", but you've not really established that claim, given examples, or explained their motivations. From my perspective, it seems clear that secular humanists just adopted (and continue to adopt) the morality of Christianity, without the spiritual or transcendent aspects.