AC disconnect wire burned out

It was a bad connection. See how the insulation stopped melting about 6" back? Had it been a wire size problem the entire length would have been melted. And the load side of the black wire also would have been melted.
You'll need a new disconnect unless your skilled in electrical repair.

I wonder if you need to accommodate a larger breaker for your system to accept the greater amperage, or a separate 20amp breaker for each string? I don't think that wire just melted down recently, but has been been systematically degrading over time by the increased load.

Our home is 80 years old. When we bought it, we had a 100amp service panel. EVERY OUTLET in half the first floor was wired into one breaker. Cooking with a toaster and the microwave going at the same time was a balancing act, complete with dimming lights. The power we were pulling through the (then) 15amp breaker would eventually melt the breaker to the point it could no longer be reset and I would just replace it. That went on for about 10 years (I would by breakers by the contractor box) until I finally broke down and had the house professionally rewired to a 200amp service. When the outlets in the kitchen got dedicated circuits, the load was spread out and we have not popped a breaker since.

IMHO (I am not a licensed electrician, did not play one on TV nor stayed at a Holiday Inn Express) your system is overloading that circuit ability to accept the greater amperage and will continue to do so regardless of the gauge of wire you use. If you go the route of just replacing the wire, please, at least put a smoke detector above the panel. I put one directly above our inverter (the town Fire Marshal was pleased to see that).