I solved this on my own, so here’s the solution for anyone with a similar problem, because it seems to have come up a lot.
I had added my locations before I added my Google Maps API key, so I basically had to go back and re-edit all of my locations. The map on the locations page checks the form for changes as you tab through it, so I just basically deleted one part of the address, tabbed away, and then re-added it, and the map rendered. After this the map search worked to, so the geocoding probably put the coordinates in the database.
This probably wouldn’t have taken so long for me to solve, but the one thing I hadn’t tried was creating a new location after setting the API key. Hope this helps someone.
Update on this. I am now getting successful responses logged in Google’s API console, but still no maps.