I didn't switch to government until the beginning of my third year, so your first sentence is a little scary to me. How did those situation arise? I feel as though applicants from those universities would be aptly prepared.
I'm currently an undergraduate at a T3 school in the United States. Does this at all give me an advantage in applying to select T10 political science PhD programs? Additionally, am I at an advantage if I apply to the same university that I'm currently attending (even if incredibly competitive)?