I decided to give that linerless tape a try since I could pick it up locally for cheap. That stuff works very well. Time will tell how it holds up. So far, I've done the branch that goes from the bulkhead connector to the starter relay and relay panel under my battery. Now, I just have to do the branch the goes to the passenger side of the engine bay. The key, as I learned, is to keep pulling it as you wrap it to keep it tight.
First picture is the before. Second is the after, obviously. Thanks again for the ideas, guys.