Thank you both for the input. On the networking question, I guess my answer is “kinda, but not really.” My two main UG profs will gladly recommend me, and they both did their graduate work at highly ranked programs. I also have another potential recommender in a peripheral area (legal theory) who has some sway and name-recognition in academia, I think. But overall it’s not like I have someone who can pick up the phone and call any of these programs saying “you need to admit this guy.”