I think my original estimate of 6-10 parts wasn't too far off the mark -- we're probably looking at a minimum of 10, though, and it could be a little more than that.
I decided that posting it in parts might help keep me going, although over the past few days the last of the questions I had about the direction in which the fic was going have been answered and I feel confident that I'll be posting a minimum of 2-3 parts per week. I expect there to be somewhere between 6-10 parts.