Ok, so an update:
Just got my new charge port in today, and I can say without a doubt that my problem was the charge port! Popped the new one in (I almost laughed at how easy it was compared to replacing a cracked digitizer), and right away I noticed that the new port sort of... kept the cable plugged in better. It started charging instantly as opposed to the game of getting it to sit just right, and my computer immediately started to install drivers.
Hooray! Now I can fastboot again! And actually transfer files from my computer to my phone easily! And actually charge the damn thing without feeling like I'm trying to find its g-spot.