I really wish you the best. Marrying someone is a big step in life. You put a lot of hopes and energy. It's understandable you want to fix your situation yet when it comes to marriage a paper means nothing and it can bring more problems than the original target. Responsibilities come first and then benefits. You cannot get a benefit when you both are not taking on the huge responsibility marriage carries.
If you want to save your marriage you and your wife could go for counseling, try to work things out and if time proves that you really want to be together then applying for the GC could be an option as long as you can prove that you married for the right reasons.
If you go ahead with her "help" she can easily change her mind. Like everybody is saying it is fraud. You will have the stress. Is it worth it?
Wish you can work things out for the right reasons.