Advise to reappy EEA permit??

Hello everyone,
I really need someone who can give me advise to reapply my EEA permit.

My questions:
How to prove that our marrige is not mariage for convenience?
Can u guys pls list me any documents i need to submit to prove our marriage is not convenience. What should i write to explain why we decide to get maried after got refusal in the cover letter?

My case is:
Im nonEu and im holding the residence card of a family member of a european union citizen.
Im in the durable relationship with my Czech boyfriend. We are in relationship for 3 years and have lived together for 1 year.
My boyfriend got a job offer in the uk so We applied eea permit about a month ago then i got refused.
In the refusal letter, the eco said i have failed to proof the durable relationship as an unmarried partner. They see the date in the tenancy agreement that we had just lived togther for 10 months, but i stated in the form that it is about 1 year. So, eco wasnt sastisfied as im an EEa family member.

My idea to reapply:
We decide to get married ( because now we cannot live together(eco sereprated us) so get married is the way to skip to two years of living)
We choose the wedding ceremony which is has only groom/ bride and 2 witness ( as the council required) . The bigger wedding might be in the future.
At the moment, i have to live in czech alone because my boyfriend has to start his job in the uk. We can contact only through facetime, facebook ( i do the screenshots everytime we call)

I really need helps from everybody. I dont want to fail one more time
Pls help me.
Thank you.