Securing house numbers to stucco
Based on other Googling, I found I had two choices: big holes through the stucco, plugged with silicone caulk and screw anchors (if I needed to hang something heavy, I definitely would go that route) or Loctite Stik'n'Seal Outdoor Adhesive.

So I Stuck'n'Sealed 'em.  Note to anyone who goes this route: it seems to take FOREVER for the glue to set!  If I had this to do again I would definitely invent some sort of rig to clamp them to the wall while the glue sets.  Also, one of the digits ended up in a very uneven section of stucco; the lower two-thirds are flat against the wall, while the top is about 1/8th" proud.  I'll definitely need to go back to that with sealer...

However, for the time being... so far so good.  If anyone else has a similar problem, this is what I'd recommend.