French spouse visa for New Zealander with U.K. Visa

[Ggoa]

Hello all, hopefully someone will be able to give me some information.

I am a New Zealander, I previously had a U.K. Ancestry visa but was mostly in France and traveling during that time. I was in NZ For 2015, during that time I applied for a French visa (I think compétences et talents), but was denied. So I got anothe U.K. Visa, this time the tier 5 youth mobility.

I have been in France since March 2016.
My French partner and I got married in Gibraltar in June 2016. my UK visa was only stamped in December 2016 when I visited London. My U.K. visa ends August 22nd, 2017.

As we were not married in France we are required to get a transcription d'acte de mariage from the French consulate in London, I was told this would take up to 6 weeks but they have just told us it would take minimum 4 months. My first question is : in order for me to be eligible to apply for the French spouse visa from U.K. (Because of my U.K. Visa) does there need to be at least 3 months remaining of my visa?

Secondly, on the TLS website (outsourced company for French visa appointments in the U.K.) it says that if you have an EEA permit writes on your U.K. Residency card then you don't need to get the visa, you can just go the prefecture with the appropriate paperwork. Is there any way I can get this permit in order to bypass getting the visa?

Not being able to work for at least another 4 months is a huge problem for me.

Additional info: my husband and I have proof of living together since may 2016, with the names on our electricity bill.

I suppose my big thing I'm trying to work out is if there is anyway around having to wait min 4 months for this transcription d'acte de mariage. This delay was not at all foreseen (i should know better by now as this whole process has been chaos).

One more thing- as I understand it I am legally allowed to be living in France with my husband right now even though I have overstayed my Schengen visa? As long as we have proof we are married, as I understand it he has the right to live with his spouse in his country.

Thank you!!