Same issue here... I've already called support a couple of times and they don't seem to care about helping us figure out this problem.
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Coming back to share my experience... after trying many times from both the Developers app and the website I was able to enroll today after 2 days of frustration. I'm not sure what made it work but I called many times Apple Developer Support to ask for help without any luck. My last support contact told me to send some information over email to look into the issue but I still haven't heard back from him. Just now I decided to try again the enrollment process and it went through. Whats interesting is that I used the first Apple ID that I tried to use for the enrollment and got rejected and even support told me that it wouldn't work. They said that I needed to try with another Apple ID, so I think my last support contact has nothing to do with my success.
My best support experience was when I used the App feedback support...
Go to Contact Us > Feedback and Other Topics > Apple Developer App Feedback.
My advice... keep trying from time to time from both the app and website and don't give up.