Star fangled nuts are part of a Threadless headset, fork with a Metal steerer tube..
never use one in a Carbon fiber steerer tube fork.

Seems like you shopped past your mechanical abilities.


You should forget parts on hand, and look for a different expansion plug system.

there are many that expand into the ID of the steerer as step one.

then as a separate thing , there is a second screw to pull down
the top cap, to compress the whole collection underneath it
stem and spacers, with the top bearing race at the bottom of It.

I tie a rope around the fork and the down-tube,
to hold the fork in the frame ,
when the bike is Up on the repair stand.