Just in case anyone is curious, I did get the issue fixed. I first tried to break the Google contacts sync by revoking OAuth permissions for Windows on my Google account. After doing a fresh log in across all devices, no change. Other devices synced without incident but the Elite x3 was still not syncing.
I ended up doing a hard reset and ensuring that the contacts sync was successful before downloading other apps and setting up other accounts.
Kind of odd, but just a heads up if anyone else experiences this!