1. Get a 1/2" end mill and chuck it in a 1/2" router. Make sure the cutting length is longer than stock thickness.
2. Attach some plywood cleats to the two pieces to be joined. Space the two pieces 7/16" or a little less apart and secure with the cleats (one side).
3. Tack a straight edge along the gap for the router to guide on.
4. Run the router down the gap.
This will remove a very minimum of the stock, and any variation in the straight edge wont matter, as the gap will be exactly 1/2" across at any point. Make sure to put witness marks every so often so that when the cleats are removed, the two pieces come together in the same position as when trimmed.