I'd make sure the ground cable from the battery to engine is making good contact. If you battery is in the trunk, there will be a large ground strap running from the engine to body. Being bolted together isn't good enough, the connections need to be removed and cleaned while checking the crimp on the terminal for corrosion.

Make sure the wire from the alternator to battery is good ( might run to the starter terminal ) . Does this alternator mount with rubber bushings? I've seen a missing ground strap cause charging problems on other cars.

Past that, find a way to full field the