Realistically the only guaranteed shot is to bite the bullet and get married. If you do it right, you should have your green card in a year, get that and you can do basically anything except vote.

They will run you through a ringer and extort a little here and a little there, all in some assed attempt to prevent fraud, why it takes a year to do ten minutes of paper work. Stay married for five more and than you can apply for citizenship. They can't deny any citizen, your girlfriend, the right to choose a mate, but they sure can make it mighty miserable. She will have to initiate and do the process. Stick to their written script and you will succeed.

I'm assuming you actually want to marry the lady, and she you, otherwise don't bother.