Ah, I didn't realize you could roll Spine back to an older version from within the settings. Thanks for pointing me in the right direction!
For future reference to anyone else who might be experiencing the same issue, these were my exact steps to resolve it:
- I downloaded the latest Spine with the updated certificate.
- I opened Settings in the main menu of Spine, and switched Spine version back to 3.7.94.
- I restarted Spine and allowed it to download 3.7.94.
- Finally, I tried exporting one of my animations and verified GMS2 was able to import it successfully.