Does EEA FP (6 month) allow to work? Need advice

I'd like to say thank you guys first.

My background information and my ongoing EEA2 & EEA1 joint application is here http://www.immigrationboards.com/eea-ro ... 92088.html, my re-apply might face delay or unknowing problem again as after 2 weeks waiting, nothing at all - no acknowledge letter/email for either of us

As I am in the middle of few recruiting process, which went fine so far with some positive feedback, I might soon need a COA letter to prove my right to work to my potential employer before I can be hired. However, I now can't trust Home Office can do their job appropriately (based on horrible experience on first application). I might do not have a COA paper in time. So I'm thinking alternative...

Does EEA FP (6 month) allow us to work? If so, should I go back to Paris, where I have lived and still have residence card, to apply another EEA Family Permit and use this to prove my right to work?
Would this application affect my current EEA2 application?

I'd like to hear anyone's opinion, or if you know where I should consult with and can get a sure answer, let me know.
Because if I do this, I need to take my passport back from my current application, and find a place in Paris to live there for more than 2 weeks to apply and get this visa, it would cost me a fair amount of time and money. So I want to consider it carefully before making decision.
Thanks everyone who would read and reply.