If you think that's bad you should see some of the construction equipment I work on (5-10 years of taps,tape,twisties,different wire colors etc). I could spent 1hr to get the part on, and 5+hrs fixing the wiring.I would say remove the electric tape and look for and bad spots first(butt connections with bare wires coming out, twisted wires, worn insulation etc.). bentd the wires around a bit and look for cracking insulation, if it is replace it, if not proceed to step 2.
You could use split loom, or stretch loom (will require the moval of wires to feed through it), repair and bad spots and zip tie or wire clamp it as far away from any major heat source as you can get it. Also tie it everywhere you can the less the harness moves the less rbbing you will have. As for quick connects I use th GM style weather seal plugs, you can buy small "kits" at most auto supply stores. They work well and last for a very long time, you can get them for 1wire all they way up to 10 wire (for more use 2 or more). Hope that helps.
http://www.whiteproducts.com/connectors.shtml ( just a web page to give you an idea of the weatherpack terminals)
http://www.cabletiesandmore.com/BraidedSleeving.php ( web site to see braided wire wraps)