Figured it out. For anyone that has the same issue-
Login to your T-Mobile account and go to the "Phone" tab. There should be a section for managing SIM cards- click through and you can enter the ICCID listed under Settings->General->About. That will let T-Mobile know to associate your phone number with the new SIM card. For good measure, I entered my number in the "My Number" section of the phone settings- but I'm thinking that might not be necessary.