They make a swivel stud set to do exactly what you wanted to do, there's a special nut that's included with the set that you drill a shallow hole for in the barrel channel at the desired location, it has straight knurls on it to keep from turning. Then a hole is bored for the machine-screw threaded stud through the rest of the stock. Cut the stud to length and dress it off and the job is done. If you do a bunch of this stuff, both Midway and Brownells have special bits to keep from lifting chips and mucking up the stock when drilling both the holes for the machine screw studs and wood screw ones. Twist drills will do this on figured wood. These same machine screw/nut stud sets can be used on hollow plastic stocks, the one side of the nut is rounded so it fits the bottom of the stock pretty well inside. When I need these, usually somebody has the sets at the local shows for cheap, stainless or blue.
You got the job done, but kind of reinvented the wheel there.
Uncle Mike's - Single Pack Swivel Screw Item 115B You can't really see the nut contours, though.
Uncle Mike's - Step Drills for Swivel Mounting