On cap, mark everywhere with pencil then sand down. When all pencil mark disappears, the surface is relatively flat. Scrape with scraper or bent razorblade to create smiling face for glue to stay.
Same process on root.
Glue cap on root, use screws to clamp them together. The pilot holes on cap are larger than screw body so the washer and root squeeze cap in between tightly.
The next day, remove screws, drill and dowel screw holes with next size up dowels available.
Use a router to remove hang-over of the cap, bearing rides on the root. Lesson from this process: (1) better glue joint with go-bars (2) much better if trim the ends to fit before hand.