I was physically robbed and now can't manage my Apple ID... how can I extract my purchases?
The way this is supposed to work is to log in to https://appleid.apple.com and have several devices for authentication.



Have you double checked that you don't have SMS as one of your options? If so, you can just get another SMS capable cell phone from the carrier using your number and be able to log in to reissue a new recovery key.

To paraphrase the KB article - http://support.apple.com/kb/HT5577


  If you lose permanently access to all of your trusted devices AND your recovery key, you will not be able to use that AppleID. 


Hopefully you can either recover your phone or the wallet (police report and/or reward work in different situations) after a few days and add in some more items, regenerate your recovery key or disable the two-factor security on your account.

Also, you will want to make a phone call to developer support and ask if they have any way to assist you in enrolling another trusted device so that you can continue to do business with them. The developer program has far more ability to tell you from a random impersonator due to the legal forms and verification you may have filled out to enter the program and sell an app.

Also realize that Apple intentionally set this up knowing that some people would be in your situation and make sure you acknowledge that they don't have to help you out, but if they can find a way to, you would really appreciate it. However, since you have thousands of dollars at stake, I can't imagine you wouldn't be able to call into developer support and work with them to regain access as a one-time exception to the policy. Heck, Apple might be able to assist with a letter that corroborates a police report of the theft and open up options to claim this against insurance.

Lastly, check with your insurance since the cost to re-establish your accounts and purchases might just be covered. Your sure move is to get a new AppleID move on, securing it with more layers (and spread over more than one location) of verification devices. Hopefully, you can recover one of the items that was stolen and avoid the lengthy process of convincing either Apple or an insurance agent to help you out of this understandable but painful predicament.