I take Keith's Radial file, then de-feature and shell the base shape. Then I can join the shelled result onto the top detail:
This is leaving the detail at a larger depth. If that little extra material "Just had to be removed", I would handle this by keeping the original "Spoke" pieces as they were before the Boolean. Most likely these can be shelled as separate objects. They can then, at this stage, be Boolean cut from the underside, to create that part of the shell.
The depth of my shell was a bit greater than was mentioned (.03125). I would have had to remove the cuts between the spokes, then recut them after, because they are deeper than that.
