Alright, seems like I'm almost there. I completely redid 12, 13, and 14. No noise or anything from there any more. I have not seen or heard a single pop/spark/etc. in quite a while. I'll keep my eye on it, but so far so good.
However, I still hear that ringing sound. Here's a little more detail. If I knock on the desk that the crack is sitting on or even type on the keyboard on the desk while no music is playing, I can hear ringing in phones. Sometimes it's limited to the right, but sometimes the left. It sounds similar to making a wineglass ring by rubbing the rim. Sometimes it will hang around for a while, but sometimes it will die out fairly quickly. It's more pronounced if I tap the volume knob, headphone jack, or 12au7. I can jiggle the 12au7 in the socket a bit and that will sometimes quiet it down for a while and make it a bit less sensitive to tapping.
Is this still seeming like a bad connection/solder joint problem? or is a bad tube possible? I'll repair anything I need to in the circuit, but am trying to avoid excessing poking around and potentially causing further damage.