If your existing harness is "melted" then absolutly yes, no question, replace the wires. Honestly $180 is cheap to put a whole electrical system into your jeep and you will spend more than that.
My real suggestion would be to buy a factory fit harness from painless that has most the connections needed. since you are replacing it anyway, do it right, and know that it is done well. the fuse block has a bulkhead connection that goes through the firewall, and connects to the engine harness (that also comes with it). it makes a nice clean connection and is not hard to install. all wires are labled to where they go, and color coded correctly (for the most part)