Thanks @skeller for the tip!
It does look like it would make more sense to put it there. I’ve put it so that it installs at /usr/share/icons/hicolor/scalable/apps/alpha-aligner.svg.
This hasn’t solved the problem though, since the icon still doesn’t show in the Dock. It’s strange, since I can drag the Activities icon into the Dock and the proper icon will show. When I open the app, however, there is a new gear icon that appears!
Here are the two icons, one above the other:
I’m wondering if this couldn’t have something to do with the way I’ve structured my program with Gtk.ApplicationWindow?