I realized that I had some old, legacy cron jobs running from WooCommerce, and the GeoIP updater only appeared with this plugin. I cleaned them all up via the WooCommerce Tools in the Status tab, and now the old cron jobs have disappeared.
I also created a new license key, and everything seems to be working now.
Thank you very much!
Probably save if you are a single-user. Still hope this is getting fixed asap!