After cutting the pivot rod out with a zip cut on a dremmel, I was able to tap each end out with a punch. Now that I have the plastic handle separate from the bracket, it is obvious what was causing the sticking. The pivot rod was rusting to the bracket as well as binding on the plastic. I'll post up a picture when it is done. I'm sure I just permanently solved this problem, and it won't require constant lubrication anymore.