Step 2: Cutting the mortise
Once the mortise has been routed out, remove the center section by drilling a hole in each corner and joining them with a jigsaw. The resulting mortise can then be tested for width and length.
The next step is to peel up all the pieces that had made up the template, both on the table and in the center rectangle that you've cut out. You'll want the router base to move easily across them, so make sure you remove all the tape residue. (I found that acetone and a razor blade made it a reasonably easy job).
Remove the guide bushing and the bit you've been using with it, and switch to a straight bit that has the same radius as the insert plate. Position the pieces of template to guide along the side of the router, preventing it from cutting farther into the table top, and then take another pass with the router, cleaning up the bottom of the cut, and making properly-rounded corners. Once done, the plate should fit neatly into the hole.
I made one more pass, with the guides set 5/8" closer to the mortise, and the bit set deeper, to make a cleaner edge on the lip than had been left by the jigsaw. This isn't necessary, but it's little work.