There's good news and bad news in my rpely to you.

The good news is, should you apply for the EEA Family Permit in the UK Embassy in NYC (which I did when I was still in DC), it will only take them 5 business days to process your application, granting you gave all documentary evidence that they need. I'm not sure if you can apply in person though. Also, getting married in NYC is a good idea, so that you can get the marriage certificate from your local city office right away, which you would need to attach with your application for the permit.

The bad news is, when you do apply, you will have to submit your passport in the application, thus it is highly advised that you send it in via special or recorded delivery. I sent mine for 2 day delivery with signature confirmation and return card for signature. I think I had it insured as well, just in case. So, if you have travel plans, and if you can go to Germany without a visa (since you're a US passport holder), then do so. Process your EEA Family Permit when you DON'T have travel plans as you won't have your passport.

But then again, if you have it processed in NYC, then it shouldn't take you long to receive back your passport with the permit in it.