Well, I finally worked up the nerve, after months of reading scary tales of routers and the damage they can cause flesh and materials, to do a 3/4in Round Over on the edges of my upcoming MAME build.
And I have to say, well.. that was easy.
I moved in the right directions, kept the base flush with the material, sanded areas I feared the router might skip on... and the round over went smoothly, quickly, and without issue. Even got the depth right on the first pass. I am amazed at myself.
Thank you all, every voice both positive and wary, for helping me do my first router cuts without incident and without injury.