As you will see, this is my first post. I am a long-time lurker, but decided to post because you are in a position to really change your situation. Most of us are not. Most of us have made the commitment through marriage, have kids, and have an "investment" in our spouse. While we can tinker around the edges, most of us look back and think, what if...
It sounds like your fiance has issues that go well beyond the SSM ones. For most of us, at least things were good early on and in your case, that is not even the case. Dude, all I can say is END IT! Period. End of story. Telling her you want to postpone and trying to make up the next day is, sorry to be so harsh, pathetic. You know in your heart what you have to do. Trust me, do it. While you will certainly be sad and maybe even regretful in the short term, you just have to trust me, you will be happier in the long term.
One more benefit. Next relationship you are in, once she finds out that you were willing to call off your wedding because your previous fiance didn't meet your affection needs, will likely be better at it and know you mean business. As George Costanza said "you will have hand."
Sorry that this is not the answer you sound like you want, but it is the right answer.
Me; 42, W; 43 M; 16 yrs S12, D9
3/13 - "I want to move to XYZ City (four hours away) and it might be without you, not sure" 5/13 - "Not sure I meant that"
