Azure App Service is a service used to create and deploy scalable, mission-critical web apps.
I was able to find a resolution to my issue. It's a bit of a workaround but gave me the end result that I was looking for. First I recreated the delete resource in the original region, making sure to use the same name as previous. When I did that, the custom domain automatically showed as attached. From there I was able to delete the binding, domain, and installed certificate, which then opened up my ability to add the custom domain to the new region's Web App.