For instance here is a picture of my Beretta's Alternator and stock + wire. That is the ONLY wire that goes direct to the battery!

That wire is very small, its not even 8 ga! Its probably 10 ga at best!
Back in the day I was running about 800 WRMS off this same setup. My lights BADLY dimmed. A cap did help but didnt fully solve the problem.
This is just a public service annnouncement on why you should upgrade the big 3 and run a HO alt...