Mission accomplished. I marked the location, protected it with painter's tape, drilled a pilot hole with an 1/8" regular bit, going in reverse and then forward, drilled 1/4" hole with the brad point bit, again going in reverse and then forward. Kept speeds low and things seemed to work out fine.
Then I tried to insert the shaft of the movement through the hole. Too tight, so I ended up reaming out the hole to about 5/16" just going at slower speed. The shaft finally went through. I secured the movement with the hex nut, aligned and mounted the hands, installed the battery
, and the little clock started its circular journey.
I ordered some self-adhesive dots to mark the numbers, but they only came in gold, so I've spray-painted them black and they're drying as I type. Will install tomorrow.
Thanks everybody for all your help. I decided to celebrate with a glass or two of white wine...much more civilized than whiskey.