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The DMT6E is 1200 grit. I think it is normal that you don't get a shaving edge off of it. That's not what it is menat for. the ~1000 grit level in honing is to make sure the bevels are set correctly...

Imo naturals don't need braking in. Only lapping.

DMT's need breaking in because there might be individual diamonds sticking far out of the honing surface, and they can scratch your edge badly....

TNT is what I expect before leaving the 1000K grit. That would be comparable to your DMT6E.
After that I go to the 4K, and I hone until the scratch lines are gone.
Then I do a couple of pyramids,...