He is correct about the battery, when you hit the key, because the battery is not fully charged, it heats up the wires and causes the starter to overheat and other stuff to happen.
I wouldn't mess with that starter, get a new one,
Those wires look to be ok but I'm not there so use good judgment on wire condition.
A battery can read 12+ volts static (no load), but slam a load on it (starter is a good example, also head lights) and it drops voltage below 12volts which is normal, drops too low and things start to heat up. Release the load (stop cranking or turn off the lights) and the battery will jump back up to 12+ volts, I've seen batteries drop all the way to 0 volt with a load and jump back to 12 volts when static.
This explains a slow crank problem more so when hot, if it was cranking over good when hot but not starting and you've tried stuff I would suggest unhooking that MSD box, wire the ignition back to stock, this eliminates the box from the equation.
When you were trying to restart the car you may have been cranking the engine for an extended period of time causing the overheated wires and the starter problem. Get this cranking issue resolved first, then work on the no start when hot issue.
Let us know what you're gonna do and what you need help with.
Hope this long post helps explain some things besides the fact that I've had too much coffee.