Use the right tool for the job. Assuming the groove you need to cut is wider than 1/8" then the right tool in this case that would be a dado blade in a table saw. Failing that, a router mounted in a rigid router table. All other methods are stunts. Trying to cut a parallel dado with hand held tools not only is a stunt, it's a real good way to hurt yourself. Note that a blind dado will need to have the blind end finished with a chisel.
No matter how you cut the groove, driving a lag bolt edge-on into plywood is always a crap shoot unless you properly pre-drill the post and sign board. Also tricky unless you have some mechanism to keep the drill centered on the groove and perpendicular to the post. If it were mine to do, I'd drill the posts groove side up with a pilot hole in a drill press. Then insert the sign board into the groove and, using the hole you made on the drill press as a guide, drill the existing pilot hole into the sign board with a hand-held drill. Carefully. Then, in a drill press, re-drill the pilot hold in the post with a clearance hole. Done this way the whole thing should fit together perfectly.