EEA-2 Unmarried Partner Res Card Refused - Appeal Questions

I am 28 year old American national who is currently living in the UK (as tourist from July 2013)

My girlfriend is 29 year old Bulgarian national who is currently employed legally in the UK and presently exercising EEA Treaty Rights in UK.

We have been in a relationship since May 2012 (not quite 2 years yet). We met in Peru on a trek to Macchu Picchu in May 2012. After the trek we traveled together along with my brother for 2 months in Peru and Ecuador. She then came to the US to live with me at my parent's house in July 2012 for about a year until June 2013 (she had a 10 year mult-entry visa because her sister lives in the US). During this time we traveled to Los Angeles to visit her sister, Florida for a wedding, and Cancun, Mexico for a holiday with friends. She then returned to the UK in June 2013 because her visa was expiring and she also needed to start working for an income again. Because we were living with my parent's in the US, we do not have any bills, rent etc. as evidence of cohabitation for that period of time, although we do have many notarized testimonials from parents, my brother, friends, her family as well as plane tickets pictures etc. that all corroborate the events that took place in Peru and US.

In July 2013 (a few weeks after she left US) I came to the UK as a tourist and moved in with her. Since then we have been living together in the UK and have 2 different tenancy agreements, utility bills, council tax bills, and rent in our name as well as we opened a joint bank account from which we pay them from.

With the assistance of an immigration consultant who filed on my behalf, On 3 January 2014 I applied to get an EEA-2 unmarried partner residence card on the basis of our durable relationship. The immigration consultant said that since I was applying under EU law, that there was no specific time period required for a durable relationship and that we had pretty good evidence otherwise proving our durable relationship. On 3 March 2014 the Home Office decided to REFUSE my application. They only referenced the bills, council tax etc. from my time in the UK (which was only the past 6 months) and none of the other evidence that I submitted was even mentioned. They refused solely because the evidence did not prove we had been in a relationship for at least 2 years. They specifically mentioned a required 2 year minimum. The immigration consultant thinks this was an unfair judgement as they should not be using this criteria in my case.

2 Questions:

1. If I decide to appeal the decision, what are the chances of getting it reversed? Is the 2 year minimum an actual requirement they can use or did they give me an unfair judgement? I have been told this process could take up to 8 months or more.

2. Can I decide to first lodge an appeal of the decision, but then decide to get married in the next few weeks (something we have been considering anyways) and then cancel the appeal and apply for a resident card on the basis of being a married partner? This seems like an easier, quicker, more sure thing route that would take somewhere around 2-3 months of total time.

We want to be able to live together in the UK legally.

Any thoughts or insights on our situation are greatly appreciated!