Marriage is a emotional bond.
If she values a piece of paper telling the State that you are married more than true feelings and attitude, certainly she isn't mature enough to get things. You even proposed to her to have a religious marriage, which shows that you do like being with her, but doesn't want to be backstabbed by the vile marriage laws in your country.
Honestly, you did everything right. You didn't betray yourself nor your values. You showed her that you care about her and her feelings by letting her know that you do want to marry her and if she doesn't want to be with you in a "non official marriage" she can leave and go live her life.
Congrats man, hope everything works out for the best.