That's a very hard situation, but there are some points to consider.
First, keep in mind that your case is sui generis. As you said, and probably you're right, you got a weak LOR for political reasons. I don't know much about politics at your department, but may be the case that your professors are committed to students from the next class. It seems to me that they place very well in PhD program; so I think there is some coordination there. You did well in classes and, for some reason weren't ranked well among your peers. How well would you be ranked among students from next class who will apply? Is there any student from a previous class that applied last year? How good was him as a student and how good was his performance in application?
Try to disclosure such info before deciding to re-apply. I would re-apply!