68 Barracuda Formula S 340 car Charging

You need a ground strap from the engine to the body. Not really important where it is, a common place is from an empty bolt hole on the back of the head to an existing bolt on the firewall. Make sure it makes good contact to the body, scrape some paint, use star washers.

Do the alternators you are getting have one of the field wires grounded? 69 and back (with the regulator you have) needs one of them grounded.

70 up does not need the ground, has two field wires. They sell the same one for both applications, just the 69 back has the ground.