911 Antenna Problem

[KM93911]

The other day, my radio reception got pretty bad, so I took out the radio to check the antenna connection. Sure enough, the wires going to the plug (12v) were frayed and loose. I spent some time trying to fix it, but the center wire that is attached to the very tip of the connector is like human hair thickness. It needs to clear the shielded part of the cable (the ground part, I think) to get good reception. If they touch, then the radio cuts out (basically, I had the radio on and wiggled the wires around in the connector to see how this all worked.) I concluded that this is one of those factory parts that when it goes bad, it just needs to be replaced, not repaired.
Here's what I'm wondering: Anyone have any experience replacing the antenna cable in a '93 911? I found other posts about simply putting an aftermarket one in the trunk, or running speaker wire as an antenna, etc. However, I have the antenna windshield, so if I do that how does it affect the booster? I believe the small black wire currently wrapped around the antenna cable going into the radio is the power lead for the booster. If you look under the dash, the antenna cable goes up through the firewall in what looks like an impossible place to get to in order to replace it. I know where the windshield antenna booster is located, and can see it, but can't see where the antenna goes once it leaves the firewall from under the dash. I am wondering what each does (the antenna versus the booster in the windshield) I assume they work in tandem, but radio reception sucks with just the windshield antenna--it definitely seems to need the one that plugs in (and that plug seems to be the problem). I'd like to put OEM parts in the car, but can't figure this one out. Any help would be appreciated.