Update:

It seems that, after nearly 8 weeks, the application is finally entered in the system.

As of yesterday, 6/3, the online system now gives "processing" when last 4 digits of actual SSN are entered. Until 6/2, it only listed that status when 0000 was entered, and found nothing with the actual numbers.

Does anyone have experience with scheduling an in-person appointment to follow-up on a mailed-in application?