She converts to your religion. Today was my birhtday and my husband spent the whole day at work and all night working on his notes. As someone starting residency next year and whose father and brother went through it, and whose girlfriend is about to start it I have to say that you can't be mad at him for not sacrificing something to spend time with you - there is literally nothing else to sacrifice; residency is called residency because the doctors used to live in the hospitals, and it was akin to monks in monastery. Try a variety of dates. I know, I know, this is the last thing you want to hear. As a physician buckling under the stress, my assigned counsellor who is also a church minister told me: So, what do I do with that. No lie he was one of the kindest human beings I've metbut I was afraid of getting deeper into the relationship, so I ended it. Ending sooner rather than later is much easier and less painful for everybody. You can and should share with her why you don't and never will believe in the Mormon church, and let her decide for herself, but be prepared to have that blow up in your face.
As such, it tends to attract the young and insecure. That's the difference - marrying for love vs marrying for a paycheck. Adding an interfaith element means you have many more adjustments to make. You will have to bring her down to reality.
Sorry you had to go through this, but it's for the best if she's about to leave on a mission. I was not moving with him until there was a promise and it would still take me a few months to find a job and relocate. It sounds like she's already considered marrying you and raising children in the church even with you being out of the church.
I think you need to figure out if you are willing to stay in a relationship with a man who's so busy, because trust me, it's not going to change anytime soon. This man basically tells you in a simple way within 6 minutes. I think in most situations its either you join or she leaves- either you, or the church. Joanna mentioned that our theology is rich with opportunities for second chances. This can be done. As a general authority I knew, now deceased, told me in the mid-eightiesвIf you find a good man who is not LDS, marry him. Build a life of your own but, make them your priority. She can never hang out on Sundays because she apparently spends the entire day at church. What if you are sexually incompatible. Ask questions, try to find out as much as you can.