We are going to married in Denmark around Xmas/new year time. We cannot legally marry in Israel as we are of different religions and Israel does not allow such marriages in country.
I don't understand your recommendation, the whole issue is that as of 16.7 he apparently cannot use his EEA citizenship unless he renounces his British one, he will be considered British only for the EEA permit.
We cannot apply the UK route because he does not earn enough money right now or have a job offer there yet...
Congratulations on your upcoming wedding. Pity you can't get married in Israel.
I think the UKBA interpretation is not in line with EEA regulations and with EU directives.
I understand about the issues with UK route, which leaves you with the option to go the EU way. The British embassy can't refuse giving you EEA family permit as family member of EEA national. When you apply at the British embassy (the country of destination where you going to live), you do not need to mention his British citizenship. Do the application based on his Danish one, and make sure when you are getting married that it will be done with his Danish passport (registration).
Once you're married and you translated the marriage certificate. Go to the British embassy in Israel or Denmark (from whatever country you will fly to UK), apply for EEA family permit. You will be getting it within a week to 2 weeks. Once you have it, have a safe flight to the UK.
Upon arriving, fill in the application and apply for the residence card and present his Danish passport and your marriage certificate and any other documents you are asked. They can't refuse giving you residence card, as they can't refuse giving you EEA family permit once you are married.
Good Luck!