Today was attempt number two at getting tires mounted and balanced. As it turns out, second time's the charm.
My mother and I paid a visit to our friends at a local body shop to check in on her Thunderbird, which is currently getting its engine torn apart. At the same time, I had the wheels and tires with me and they took them right in and swapped the tires while we waited.
After nearly a month there's also more room in my garage now, since four tires' worth of space has been freed. That makes my parents happy.
As the final piece(s), I just need some hubcentric rings, and these can go on!
Regarding the center caps, I've also settled on what to do with them. When a friend of mine gets back into town we're going to make up some vinyl overlays for them to cover the existing silver/black Volvo script.