Factory wiring is marginally sufficient at best and that's when it's new. You have wiring and connections that have been subjected to ~20 years of temperature changes, moisture, movement, etc.
I'd absolutely upgrade the wiring. I'd run 0 gauge from the alternator positive to the battery, from the battery negative to the frame and from the engine block to the frame. The alternator is already grounded to the engine block through it's body so no need to ground it directly to the battery negative. It's easier, cleaner and shorter to go from the engine block to the frame. Honestly, I'd bet that you'd see an improvement just doing this while still running your current alternator. If it were me, I'd do the Big 3 before changing the alternator just to see, then replace the alternator. The strength of an alternator doesn't mean shit if it's connected to a weak and insufficient circuit.
To give you an idea of how the factory wiring is marginal if not undersized, I've see drastic improvements in headlight output by just replacing the stock headlight wiring with 10 gauge, which is the largest wire that can be squeezed into the pins of the relay box. I'd just use a relay circuit fed from the battery and triggered by the headlight circuit than replace the actual factory headlight wiring in the harness, though.