I got the dash, cluster, and steering column cleaned up this morning. Amazing what some water and a rag can do.
I also pulled out the junk homemade battery tray and copper pipe wire looms. I found that the fried wire is between the battery and alternator, so I'm going to replace that and try to figure out the problem. I'm also going to replace the battery cables with side post terminals so I can easily swap in the battery from my other truck (this truck didn't come with a battery).