I spoke with my sponsor and he helped me to draft the following letter, which hits all the points I wanted to make. I really had no intention (or delusion) of trying to barter back into their good graces.
"Thank you for broaching this conversation. I sympathize with the concerns you have for (my GF) and your desire for her to have the opportunity to relish and enjoy a very proud day in her life. I agree that regardless of the long or short term outcomes of the time she and I have had living separately, we both gained valuable insight and perspective individually.
I think its worthwhile to acknowledge and accept the inherent discomfort of the situation. If I am to remain in X's life, and I hope to, it's my desire that my relationship with both of you be mended and frankly, stronger and more transparent than it has been in the past. I also acknowledge that the goal of transparency is largely mine.
Where my and X's relationship was in May and the months leading up to it and its progress and transformation to where it is now are between X and I. Certainly for the immediate future, I don't believe an emphasis or in-depth discussion of those events is appropriate or productive, and would be quite the contrary. I can affirm instead that the work that X and I have invested in ourselves during individual recovery has prompted a transformation in our relationship from an unhealthy state to one that's more mutually supportive, loving, and happier than its been, ever, or that I could have ever imagined.
I want to emphasize that an immediate resolution and mending of fences around any sentiment existing between you and I is not required, and probably not the natural course of things. If I'm to be in X's life long-term, I'd prefer that actions instead of words, serve as the primary foundation of trust for any relationship between you and I. Over time, hopefully honesty and evidence are all that's required.
(Addressing her father), I sympathize with your concerns regarding X's continued progress towards completing her dissertation amidst she and I moving back in together. It's among my greatest desires to see X standing confidently on the day of her defense. X and I have journeyed alongside one another through graduate school and life over these past nearly five years, and I believe that we share a mutual desire to see the other past the finish line. Wherever and whenever I can, it's my desire to support X in her efforts to complete her thesis for the reason that it brings me joy to do so. I am very proud of her.
All this said, I am very excited to see any member of your family that arrives in (our town) this September and to share in the joy of a monumental milestone in Xs life. Although I've not always been forthcoming regarding my feelings, I care for your family very much. Thank you for your concern and support."
I feel good about it and they responded well. My sponsor told me to avoid bragging or boasting about how I'm doing, and like the members of this board suggested, to keep the focus on Liz. I also wanted to set firmer boundaries on the input and role her parents have played in the relationship between my gf and I because in the past, they were crossing boundaries they had no business crossing. I think I achieved that as well and it was a relief when both parents acknowledged that in their reply.
Thanks everyone.