Here's part of what is difficult trying to diagnose something long distance.
You state "the only damage visible was near stereo", but don't say precisely what that was. We're left assuming what you stated before.
You've stated you don't have much experience with electrical, yet feel confident to state there was no damage inside of dash, where we had enough heat to melt some wires (although that looks like it's heat from current flowing in the conductor inside those wires), and a nearby switch was misbehaving and is potentially showing some heat damage on a circuit board, and you say you're hoping someone would say it's a bad ground.
There isn't enough information yet to know what the original cause was, nor what all has been affected. We can't see and explore the vehicle as we're not there. You're the eyes on the scene, and witness to what occurred.
You can easily have multiple issues. And some of your observations of problems can be multi-causal. They may be rearing their heads at this time just because, or because they're related to what caused the huge current flow, or related to some damage done during that.
That could be some reflow, it could be some rosin, or it could be a sealer sprayed on the board. The rug is in great focus, the board not so much so.
So to be clear on some things,
With "all wire damage was on the harness nearest the stereo", does that mean to the car's harness or to the 'pigtails' attached to the stereo?
With "the rainy night my wife turned the defrost toggle on", you had the headlights on when this happened?
High beams or low beams? (no fog lamps seen, so that's out of the mix)
Without uninstalling it, can you see any signs of heat damage (melting, black) on the high/low switch on the left side of the steering column, around the 10 am location just in behind the dash?
Now pulling the light switch no longer turns on the headlights. Where the headlights on and then went out when that wire melting occurred following your wife turning the defroster switch on?
How much delay between turning the defrost switch on and getting the smell & smoke?
> By defrost switch, I assume you mean the switch to power the rear window defrost? If so, does the wires that go to the grid on the window look good? No shorts? No repairs to the grid that would reduce it's resistance so it drew more current than usual?
We've got issues with some gauges.
> the gas gauge and the coolant gauge needles max out on high when the car is started
> My temp and gas gauge are fine until I turn blower on or headlights, then the gushes go full up
Does that mean those gauges are good when you turn the ignition on, then max out when starting, then return to a normal appearance once running, until you turn on the blower or headlight switch?
One thing you can do, which may or may not help, but should be done anyways, is redo the battery's ground to the car's body. Ensure everything is off, remove the positive cable attachment from the battery, find where the negative battery terminal's cable goes to ground to the car's body (usually from the battery back towards the shock/spring tower, be it along the inner fender somewhere or on one of the nuts on that tower). Disconnect the cable ground and clean up any corrosion. Cover with dielectric grease and reattach. Connect the positive back to the battery. And while you're there, may as well clean both terminals and cable connections to the battery and cover with dielectric grease.
There's more, but we'll start with that.