It's ok bro. If your love for this girl is strong enough, than you would never fall in love with the American chick. This will give you and opportunity to realize if you really love your girlfriend and its not just infatuation.

However, its not ethical as you said. But, if you want to go through your employer- It will take you forever. Even with DV and if you got selected this year, it would be at least 6 years from now. So, its the only shortcut that i can think of and i am not a lawyer for sure.

Just carry on the relationship with this girl and see where it leads you. Good Luck! My fiance is in F1 and i know how "status" sucks.