If you can take the top off, remove the bracing and simply reduce the thickness with a hand plane. It's quick, clean and accurate - no fancy power tools needed, just a good sharp blade. Using a router just makes the job more complicated and it's the wrong tool for the job. Sorry, but it really bugs me when people suggest power tools instead of more appropriate hand tools for a simple job like this.
I would use a trim router harbor freight has one for 30.00 pre drill your depth and go crazy on that lid. clean up wit a sharp chisel or razor knife sand if needed
Sharp chisel and tap with a light hammer.
That will work. Great job with the jig.