That definitely is a complicated situation. Unfortunately I do not have a great answer for you besides referring you to the UK Border Agency directly. With such a specific case, I really think you should talk over your options with them. The UK Border Agency site on EEA Family Permit and telephone # 0845 010 5200 will hopefully lead you to some firm answers.

Congratulations on the new job! I hope everything works out.

 

I see 2 things that need answers in your post.

Work eligibility
You are eligible to work in the UK based on the fact that you are married to an EEA National. Your right to work stems from this relationship (assuming you have the relevant documentation as proof of course). I have a sticky about this in the forum, please have a read. But to put it simply, yes you can work and your proof is your marriage certificate. This right is outlined in the EU Directive 2004/38/EC that allows freedom of movement to non-EEA nationals married to an EEA National.

Entering the UK to work
As with any person wishing to enter the UK, you will need some form of entry clearance, which can be a family permit or a straight out visa. A normal UK visa will entail fees, while an EEA Family Permit is issued free of charge. You will definitely need to apply for this again, and soon.