So I've finally got my hands on a working SubWOOFer which is another Rolling Press Mini Kit that is basically just a dog-shaped Bluetooth speaker and a small book. Can't say I'd recommend anyone else purchasing one for themselves, the quality of the two that I purchased was terrible. The first one came with the plastic volume buttons broken and its replacement (from a different storefront) had a completely broken on/off switch that I had to resolder! But it is adorable and that's what matters.
Using Spotifyd and following this tutorial, I was able to turn the Raspberry Pi Zero W 2 into a Spotify Connect player. Then I followed this tutorial to get the SubWOOFer paired and usable as a Bluetooth audio device. Everything worked like a charm, though I did run into some problems when I accidentally set up the Spotifyd service as a system service rather than a user service.
With that all sorted, the Raspberry Pi is now a functional Spotify player. Now I need to update my program to detect if the speaker is available for connection via Bluetooth and play using the local device if so, or otherwise play through a device specified in the config. That way I can easily control whether the audio is played through the dog or another device (in this case my house's speakers) by turning the dog off or on.
One last feature I was considering was using the tiny plastic tonearm as a playback controller. So placing the tonearm on the record would start the music and removing it would pause it. This might be possible if I wire in some switch to the internal base of the tonearm, but I'd have to design my own contact switch and figure out how to wire that up to the GPIO pins. This feels like it'd be a nice touch, but I'm not holding myself to it just yet.