Thanks for your reply.
I was a bit proactive and went back to the Stadthaus and dropped off a copy of my PhD approval with them. Evidently, they bundle all the applications and send them off at once, so I was able to get my extra paperwork in before they sent them off.
As for the visa stamping - I think the boarding passes are proof enough. They said it was no problem - I mean, I registered at the office so that's proof I am here. Although, I was hoping I could take a little trip across the border and back just to get the stamp.
Now - the fun of getting an apartment.