You're in a dangerous situation, in my experience. Do take to heart what SixOfNine said.
It's not apparent from your post whether Melissa was raised as a JW, but in any case the JW teachings seem to have been ingrained deeply enough that she's still a believer, even though she doesn't follow many of the teachings herself. She's obviously very confused inside, or she's the sort of person who will go against what they believe in order to get some perceived benefit. If she's that confused or that willing to act contrary to her supposed beliefs, your relationship is bound for trouble.
Many people who leave the JWs because they don't want to practice JW behaviors remain believers and wrestle with their consciences for a long time. It creates problems not only for them but for anyone they have a relationship with. The best thing for you would be for Melissa to resolve her own inner problems before you go further in your relationship.
From my own personal experience, living with a 'true believer' who thinks you're going to die at Armageddon is the pits. You can't imagine how painful it is. They don't treat you like a human being, much less a partner. They view you as a dead man and treat you the same. If you can live with the possibility that your girlfriend might turn into such a person, well, that's up to you.
Melissa's actions are fairly common among ex-JWs who haven't really resolved their inner issues. They remain believers and so, when it comes to their children, they want the kids to toe the JW line because they think it's for the kids' benefit, even though they themselves may have resolved themselves to dying at Armageddon. They might think that they're not worthy of 'getting life' or they might just not care. In any case they have enough 'issues' that their emotional lives can become turbulent, and cause serious problems for anyone with whom they have a relationship.
If you really want to continue your relationship, know this: one day, sooner or later, Melissa will resolve her 'issues'. For you it will be a crap shoot as to where she lands. If she lands on one side, you'll be fine; on the other and your life could become hell. So for your own protection, you need to figure out how to get Melissa to resolve her 'issues' sooner, before you make a long term comittment.
A lot of people on this board can help, which you obviously already know or you wouldn't have posted. Do keep taking advantage of this wealth of experience.