When arriving at this screen, the add credit card button just doesn't do anything:
This led to about an hour of frustration, trying different browsers, computers, etc. Of course, we should have just turned to our trusty Twitter account. Within minutes of sharing our frustration, the solution to our problem was right there in our "at replies."
As it turns out, everyone is having issues adding a new credit card at checkout. Luckily, the workaround is simple. The first step is to navigate to the home screen of your Yankees ticket account:
Next, click the "account settings" link, and you will arrive at this page:
From there, you want to click on the "credit card information" link, which will bring you here:
Unlike the frustrating "add new card" link on the checkout page, this one actually registers your command, and you are able to add the card successfully.
Now, when you attempt to pay your invoice, all of the cards that you added within your account will appear as payment options:
And just like that, we have a workaround for the ever-glitchy ticketmaster web interface.
Many thanks to LeoKitty, nyydem, and michebag22 (all great Yankees fans on Twitter that you should all follow) for responding with that simple solution.