Thanks for following up with a solution to the problem!
I was able to replicate your problem. (I had enabled that option many moons ago, and forgot that it wasn't on by default.)
I knew the model was a mess, but it always sliced correctly for me. You're the first to mention the error.
I have rebuilt the model so it slices properly, and saved it in STL format. (Even got the preview to show up correctly.)
Thanks again for helping me fix this problem.