Surprisingly, my PC recognized my phone (made the little USB sound) and I was able to fastboot flash-all the newest factory image on it!! No toolkits required! When it stopped blinking, I hooked my dead phone up to my PC via a USB 3 port and held Power + vol down to boot into fastboot (the battery was still too low for the phone to boot normally - it would just show the battery icon). Then I put a rubber band over the power button so the red led would blink (I wanted to completely drain the battery).

I wound up fixing it by entering fastboot and making it display barcodes until the battery died.