I didn't realize the mainstream CoC folks were of that mindset. Are you over generalizing @Kevin, or have others experienced this?
I can't speak definitively for all sects or churches within them (there is a lot of diversity) but often that is true. This is a classic stance of organizations in mid-stage decline. Although I think some of their churches have declined past that and are increasingly loosing their distinctiveness.
I hear you, but the comments in the comment section of the video render an argument or even honest debate useless. He basically says that we can't use the OT to justify anything. If it's not in NT, it's part of the obsolete old covenant done away with at the cross. It's almost like speaking two different languages. There is no common ground, other than NT. Our greatest ammunition is from OT and the support for validity is that it's not explicitly outlawed in NT. The fact that it's not explicitly addressed in NT tells them it's not part of the NT plan,
You go to Romans, where Paul teaches that the OT is there to instruct us what is sin and that if it weren't for the Law; we wouldn't know sin. That is your hook to use the OT to define what is and isn't sin. This allows you to bring up the utter lack of condemnation for polygamy in the Old Testament. Then you mirror his stance (about NT repeating laws from the OT) and point out the NT also does not condemn polygamy.
You can follow that up with (or skip all of that and start here): insist he give you "book, chapter, verse" where the New Testament condemns polygamy. When he can't, point out that Christ gives us an "approved example" in his parable of the bride-groom. Surely Christ wouldn't picture His relationship to us as a sinful one!
He will of course go to the divorce passages to try and prove his point. So be prepared to discuss the actual meaning of adultery and how Christ was not talking about polygamy but divorce and condemning serial monogamy. You may also need to point out the non-equality of the marriage commands. All of these will likely be new ideas to him.
Another approach would be to point out that David was a man after God's heart and how God offered to give him more wives. And while that is OT, you can point out that God doesn't change and God in the OT (and Christ in the NT) imagined Himself as a husband to multiple wives. He can argue against polygamy with a 'from the beginning it was not so' argument; but he can't argue that God's heart has changed.