After further investigation, I'm happy to announce we have a system in place to unify accounts between the new website and the existing game. Please follow the directions below, depending on whether or not you've already created an account on the new website (where you're reading this):
I already created my new account:
Click your name in the top-right, and select Account Settings.
On the menu to the left, select Game Login
Enter your game login details
You can now use either method to login to the website. If you change your display name or email here, it will automatically be synced in-game.
I don't have a new account yet:
DO NOT sign up on the new website (or do, and then follow the steps above).
Instead, LOGIN and enter your in-game login details. The system will automatically create you a synced account (you may be prompted to fill in some missing profile fields).
I've never played Virtual Nations before:
Click the sign up button. You will be redirected to the game UI to create your game account, which can then be used to login to the game or this website.