The ACTUAL Solution
coreaudiod (the core audio component on these older Macs) is failing, constantly restarting preventing it from running correctly. The culprit (for reasons that elude me) is Background Music, an app that I had never used or even heard of before but may have been there the entire time. For whatever reason it is causing coreaudiod to fail and for no sound devices to work correctly.
Removing all traces of Background Music FINALLY solved all of my problems, the link I used is below but I will post the full text in a comment as well just in case.
https://github.com/kyleneideck/BackgroundMusic/blob/master/MANUAL-UNINSTALL.md
Here is what to do (taken from the GitHub link posted above):
Manual Uninstall
Delete Background Music.app from /Applications.
Delete Background Music Device.driver from /Library/Audio/Plug-Ins/HAL.
Pause apps that are playing audio, if you can.
Restart coreaudiod:
(Open /Applications/Utilities/Terminal.app and paste the following at the prompt.)
sudo killall coreaudiod
or, if that fails
sudo launchctl kickstart -kp system/com.apple.audio.coreaudiod
Go to the Sound section in System Settings and change your default output device at least once. (If you only have
one device now, either use Audio MIDI Setup.app to create a temporary aggregate device, restart any audio apps that
have stopped working or just restart your system.)
Troubleshooting
If you still have the Background Music audio device, try using Terminal.app to make sure you've deleted its files:
sudo ls /Library/Audio/Plug-Ins/HAL
If you see Background Music Device.driver in the output of that command, use this command to actually delete it:
sudo rm -rf "/Library/Audio/Plug-Ins/HAL/Background Music Device.driver"
Then restart coreaudiod again. If that still doesn't work, restart your computer. If that doesn't work, feel free to
open an issue. Include the output of sudo ls /Library/Audio/Plug-Ins/HAL.
Optional
Delete BGMXPCHelper.xpc from /usr/local/libexec or possibly /Library/Application Support/Background Music.
Unregister BGMXPCHelper.
If you're using OS X 10.11 or later:
sudo launchctl bootout system /Library/LaunchDaemons/com.bearisdriving.BGM.XPCHelper.plist
If you're using an earlier version of OS X:
sudo launchctl unload /Library/LaunchDaemons/com.bearisdriving.BGM.XPCHelper.plist
Delete BGMXPCHelper's launchd.plist.
sudo rm /Library/LaunchDaemons/com.bearisdriving.BGM.XPCHelper.plist
Delete BGMXPCHelper's user and group.
sudo dscl . -delete /Users/_BGMXPCHelper
sudo dscl . -delete /Groups/_BGMXPCHelper
Thank you so much to kyleneideck for this solution.