I would remove the stud, and just drill a new hole straight, starting in the center of the counterbore ( I clamp the stock & use a drill press).
Then, liberally coat the stud threads with car paste wax, fill the now "Y-shaped" hole 3/4-full of epoxy, and seat the waxed stud, ensuring it's held square, etc, until the epoxy sets.
The wax will enable the stud to be unscrewed if desired, and the top should hide any epoxy in the hole.
( I also apply the paste wax to stock around the hole prior to pouring in the epoxy)
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