Hello, I am Rafael. Thanks for asking your question - I'm here to support you. (Information posted here is not private or confidential but public).
I am sorry to know about this frustrating situation.
I think what you've been doing already is the best way to approach and work on it. I'd just say that trying is OK, but doing it with %100 honesty and consistency is what is needed here.
It would not ensure you would stay or get back together, but it would the best you could offer for your relationship to heal and grow from it, as long as she wants to work on it.
I'd say that words are important, very important, must always be honest and express respect, love, understanding and support, but without consistent actions showing they are true, they would become useless and manipulative; then please focus on showing her through concrete actions without exceptions , that you really feel sorry fr what you did, that you have taken full responsibility for it and are willing to do everything in your power to deserve her trust, respect and affection back.
If after the first counseling sessions she asks you to leave, then please respect her decision and every boundary she sets, in that way you would show her that you really care about her and about your relationship. and that even if she chooses to end it now, that you would work on yourself to deserve her back, but only in case she happens to feel that's what she wants and not because of you pushing her at all.
Does it make sense?