If your cables and solenoid are heating up then you have a lot of current flowing and usually that indicates a short. If someone was running the starter for bursts longer than 20 seconds and not letting the starter cool down for a couple of minutes before trying again, then the likelihood is the armature winding insulation has melted.
Simple check here would be to check the commutator ring on the armature to the shaft on the armature with an ohmmeter. If there is continuity between the 2 then the armature insulation has broken down and there's a short in the armature between the windings and the plates in the armature itself.. Armature rewinding is a common practice and is not that expensive. You could probably get the armature rewound for about $100 Canadian. (It's been a while since I had this done) The other option is to pick up a used starter but you're taking a chance here. As mentioned before, the common understood among us mechanics is 20 seconds running , 2 minutes resting or pay the consequences.
On most starters, the brushes typically don't have insulation on the wires although I have seen plastic insulating tubes over those brush wires as well. I'm talking about starters in general and not specifically KZ starters.
At his point I would also suggest pulling the solenoid apart and having a look at the contacts of the solenoid. Arcing across the faces will increase the resistance across the contacts. Most contacts are just bare copper and can be cleaned up with a file and then wet/dry paper. They usually have a slightly convex face. Some solenoid contact faces are silver faced and I have had good success with building up the faces with solver solder (Sil-Fos) and then dressing up the faces. I would only do this to save a "no longer available" solenoid on a restoration. In this case, if the solenoid is bad and the contacts can't be cleaned up leaving enough material on the contact faces, just replace the solenoid with a similar one. It's not rocket science here.