Bulkhead wire 64 Barracuda
I should mention that I am using a 65 Dart bulkhead connector ...
It appears the OP is also, per photos in post 1. Sorry, I couldn't see them when I made post 10 from a cell-phone. Wonder why - modified?, late 64 with 65 parts?, Cudas different than Darts & Valiants? No problem if the ALT and BAT feed-thrus wiggle slightly in the plastic bulkhead, since that is not an electrical connection. The only connection is at the bolt in the engine bay. The cabin side is crimped and/or soldered to the 12 awg wire. All you might need is to unbolt, sand the connections and re-bolt. I coat w/ silicone grease, but battery anti-corrosion spray should also work.
Not surprising that a 30 awg fuse keeps blowing, since that BAT wire carries the charging current from the alternator (up to 60 A, depending on alternator). Indeed, it carries all current flow in or out of the battery, less transient underhood loads (starter & horn). While upping the fuse, you might re-work that gomer'ed wiring. There shouldn't be any exposed copper and strange it has 2 butt crimps where none are needed, plus those things scream, "amateur".