Eureka, I've got it. I was able to install the older version of the plugin and it worked for me. I had to jump through a bunch of hoops to do it, but I think we're in business. I just logged in and linked it to my existing wiki account even. For anyone who might be interested, I had to install the Google API Client separately using composer, which was a new thing to me, to get it to work.
As a bonus, we're running the latest Media Wiki now (1.28)... @Bez if you wouldn't mind poking around to make sure I didn't leave bork anything in the process content or plugin-wise that would be cool. I installed a different breadcrumb plugin, for example, since the one we previously had in there is no longer being maintained.