How do I become more in my body while training?
Strength fundamentals have little to do with actually lifting weight.  There is a lot more to be said for knowing where your body is in space, what it is doing under that load, and how to create and apply tension in a useful way.  The issue of developing a platform to allow for individual exploration and improvement in movement quality, is that people are rarely in their bodies.  They go through the motions, but are far from the reality of being aware of their own bodies in space.  This is made all the worse by the addition of regular checking of a device for a distraction from that moment.  The irony of which, is in no way lost on me.
To be in your own body.  To be present.  This is something that is a challenge to teach or express.  Yet, can you codify play/exploration in a way that becomes useful at some level, that doesn’t strip away the value by trying to guide a path towards it.  Being told to play is lost upon people, suddenly an exploration of movement becomes a filming opportunity, or a spectacle for someone to heckle.  People are often no more aware of what they are doing in a cartwheel, than they would be while lifting weights; the latter is at least familiar.

The answer in the past has often been one of loading.  That with enough load you could force people to show up and pay attention.  That they get too scared of failing to be anywhere but present.  Yet in that scenario they can be caught up in fear, worried about failing, not knowing what is expected.  So how does one prescribe and teach movement in a way that is present, that has more to do with a growing awareness.  In reality, I think this is something that can only be experienced after a certain amount of self knowledge occurs.  The lesson of full awareness is a hard one to teach.