Thanks very much for the kind, thoughtful answers.
The torrential Michigan rains continued until last night.
Once things dry out a bit, I'll inspect what's left of my radish crop, and act accordingly.
Judith -- Thank you for qualming my fears. I've since found the forum with explanations for newbies like me, and am feeling more at home. It's a neat place, this Permies forum!
Kelly -- Thanks for that silver lining.
I'll keep this in mind, for future ant issues. I'm still hoping to eat a few of these radishes, though...
Jay -- Covering them after laying DE is so obvious, I missed it. THANK YOU for that suggestion!
I do have toads and a few frogs in my garden, and will research how to provide habitats for them. They seem to like shade (and so do I). I also have a few garden snakes and a sneaky fox squirrel.
Fred -- Thanks for the boiling water tip. I considered this, but was hoping to save the radishes these ants had nested beneath. I lived in Texas for a number of years, and we were plagued by fire ants. They're awful! I'm glad I'm just dealing with little pavement ants.
Again, thanks to all!