Since this started with the fork installation, let's start by eliminating the headset as a problem, especially since you're concerned about the split cone.
The test for a headest is very straight forward. Either lift and drop the front wheel and listen for the klunk or bump of a loose part (the fork). OR, apply the front brake and rock the bike forward and back feeling and watching for play at the lower bearing.
If the headset is loose, it might be that the spacer stack is too short, so even though you're torquing the screw you're not able to tighten the headset because the top cap is bottomed against the steerer.
Otherwise, you're hard braking vibration might be things like a dirty or oily disc rotor, or lack or rigidity someplace along the line. Sometimes new brakes are a bit finicky and simply need some time to settle in, so if you don't find anything, give it a short while.
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