Matt,
I gotta be honest, that seems like a dangerous way to try to accomplish something. I just realized that I have no idea what the goal of this conversation really was, to see if your clean is a "bad" choice or if it's a way to train RS, or even something else? I'm just going to go ahead and lay out how I see it for you and anyone else who willing to read this, and this is coming from me and only me with an undergrad in Athletic Training, Master's in Physical Therapy and years of study and practice. It's loaded with lots of opinions and no references (proceed at your own risk).
Reflexive stability is an unconscious anticipatory/reactive activation of muscles. It should come on whenever we have to work against gravity or other external force. This means during sitting and standing at rest as well, because gravity is that constant force we're always working against, "loaded" or not. If we're talking specifically about the "core" well I think of the core as the muscles that have a direct connection to the spine and/or ribs. Yes, I understand that this is a lot of muscles. And yes, if you follow the idea of Anatomy Trains, as I do, then essentially that means that just about every single muscle (skeletal) can play a part in the spine's reflexive stability via attached musculature. Pain will cause the body to try to turn off potential sources of that pain and the body will use larger muscles in a supportive fashion in order to splint the painful area. This accomplishes the goal of removal of pain, but doesn't necessarily fix the source, unless that bracing allows healing. But pain is a powerful teacher, once we remove the pain, we have to remind the body that it can use those smaller stabilizers and stop calling on the larger ones, unless the external force requires it. That's how I see OS working and how they market it: you're reminding your body how it was meant to move.
But aside from pain, why else would we have forgotten how to move? We live in a very physically supportive world. We have bucket seats and orthopedic shoes. We have exercise machines and special chairs and benches on which to sit and exercise. We've eliminated many of the physical challenges that the body needed to be ready for. This is not why we have this fantastic, multi-segmented, highly complex package of nerves, muscles and connective tissue we call a body. I have gone completely off-topic, but honestly, I'm not seeing the point of most of this thread.
OS works. Kettlebells when used properly work. Barbells, gymnastics, yoga all work. If you are finding a limitation in how your body responds during an exercise, there are many, many reasons why that might be the case. Maybe you need a different challenge. Maybe you need to let your body recover more. I can't say from here. I don't say any of this in a way that you or anyone else can't argue with Brett or me on any topic, but I'm reminded of a person who argued with Dan John on the proper way to do a goblet squat. When it comes to the goblet squat, Dan is the man because he invented the exercise. Someone may have done it before him but he gave it the name and made it popular. So while Brett or Gray may not have invented RS, they are leaders in the area and have helped to define what it means, how to assess it and bring it back. So when it comes to goblet squats, I defer to Dan John. For reflexive stability, look to Brett, Gray and Lee. So Matt, if your clean is helping you the way you want to, that's great. But if Brett says something isn't RS, then argument is over from my point of view.