Hi @george,
Sorry for the late response! After taking a peek at your model and playing around with it, I was able to create a screencast showing my workflow (based off of yours) that can create that tight hexagon on the top of the crown. The reason, as you somewhat hinted to in your post, as to why it wasn't lining up was because it wasn't exact. The biggest factors that influenced where the points on the hexagon lined up were the size and distance of the hexagon, as well as the width of the rounded part of the crown.
What I did to recreate your crown was to first project the scaled body from the .f3d that you attached in your post into a sketch so I had the general outline. (Recreating that by scratch would've been tough!) Also, the reason I projected the body geometry as opposed to using your sketch, was that you scaled the original body to a larger size. This just saved me some steps. Also, your sketch geometry was not perfectly lined up with your plane that the base was created on, so this caused a few overlap problems as well. In my screencast I saved the projected body geometry as a .DXF file and uploaded that as a Fusion Design and opened it. Then I aligned the center of the sketch with the origin (this just makes things easier to visualize in my opinion). Then, I created a new sketch on the plane where the base would be and projected the sketch geometry of the imported sketch (the curved crown part) onto the new sketch plane. This allowed me to see my end points so I could sketch the base. Once the base was sketched I then created my hexagon on the base (this will allow you to manipulate what size you want the inner hexagon to be and from this you can figure out what width the curved crown parts should be.) I know that was probably confusing to read, so please enjoy the screencast!
Hopefully this answered your question! If you have anymore questions, please don't hesitate to let me know. I'm more than happy to help!
Thanks,
James Youmatz
Product Insights Specialist for Fusion 360, Simulation, Generative Design