For the starter issue, it occurred to me that all my testing has been done from the cable connectors, and not the battery itself. I've cleaned the connections a few times, but I wonder if they connectors are just that ****** right now, that even when I hooked jumper cables from the battery to the starter that it's causing a drop in voltage.
To answer my own question here, if it was the connection to the battery, then it should have helped when I tried to jump start it the other day. I am leaning towards the wire between the solenoid and the starter relay at this point.