Thanks for all the advice, yall!

What kind of glue do you recommend? I've got on hand some Titebond III
and Gorilla Glue, as well as some Elmers regular Wood Glue.

I suppose I could pick up something like Liquid Nails, but I've never
used it before.

"Good way to do this is to use an offset router base with handle, and
clamp a
thick board to the opposite edge, even with the top of your edging, to
give
you a stable platform ... be sure to route in the proper direction so
the
router doesn't jump away from you."
All I have is the standard PC base and the plunge router base that came
in the pack I bought, and I'm not sure SWMBO will allow another
signifiacnt tool purchase for this project. Are offset router bases
expensive? (i.e. more than $50? :-) )

I think if I can clamp some scrap 2x4s I have lying around to act as a
support I should be OK as to the stability of the router.

-Nathan