If you disconnect the alt, does the problem go away? This might be a simple test to see if it is the alt that is giving you these problems.
This really sounds like it could be a bad ground too.
+1 Check your ground(s).
67 fastback
351w
Baer brakes
G-Force T5 trans
9" rear w/3:50 gears & 31 spline axles Link
Recently moved Salt Lake City from the SF Bay area.
Looking forward to driving on the Miller Motorsports track this summer!