Men and women are both carriers. Since men cannot be tested for it, most sexually active men are carriers because they have no idea they have it unless there is a genital wart. Do not assume you infected her. If she wasn't a virgin when you met her, she could have gotten infected years ago. When sexually active people have sex, there should not be any finger pointing on who infected who. It is impossible to play detective with this virus. No single sex act or partner can be identified unless you slept with someone who has visible active warts. You should assume that you have what she has. I don't know of any therapy for men in the Western world. Strain 39 is a high risk for cancer strain, as you know from the pink book.
There is a low risk (5-8%) that one day (decades from now) that you can develop anal cancer or penile cancer, etc. You can do is to see a urologist and a proctologist for yearly exams. You can also live a more healthier life to boost your immune system by quitting cigs, reducing alcohol, getting more rest, reducing stress, exercise, take vitamins,etc.
During her recovery period, use condoms so she can recover quicker or give her a few months of no sex to recover. After that, you two can have all of the unsafe sex you want for the rest of your lives because you cannot re-infect each other. There is no ping pong effect. Stay monogamous with her forever and enjoy sex without any guilt.