I'm not entirely sure of the context: do you want to cheat on her with the woman she was in the past, or do you want to cheat on her with someone like she was in the past?
If it's the first option, then I'm not sure about "a girl". You're talking about someone specific (who she was), so "the girl" seems a better fit.
If it's the second option, then "a girl" makes a bit more sense, but you'd need to ensure the reader understands the context.
In addition to the clarity issue in your question, in both cases I'm not sure about the placement of your ellipsis. It breaks the flow at the beginning. I'd rather shift it towards the end of the sentence.
So, to achieve your objectives, the first option could be:
I think about cheating on you with the
girl I remember. The one I had
romantic moments with, who seems to no
longer exist ... the girl you were,
when we first met.
The second option, which is similar:
I think about cheating on you with a
girl like the one I remember. The one
I had romantic moments with, who seems
to no longer exist ... the girl you
were, when we first met.
Also, my personal preference would be to drop "when we first met", and just leave the last bit as "... the girl you were." Seems to carry more punch.