The wire size I mentioned for the bond for the cold-water piping was just given as an example, assuming two conductors per phase. You most likely have more than that.
Basically, you would total the Circular Mil Area of all ungrounded conductors for one phase. Then use table 250.66 to size your grounding electrode conductor. Sounds like you could be okay there.
You would normally do the same for the bonding jumpers for the cold-water piping and the building steel.
Generally, as I read it, that #6 Cu would only be good when used as the sole [only] connection to the ground plate or rod when it is used as a supplemental ground. There may be other issues, but it seems likely that these could at least be part of the problem.
Just FYI, The Soares book on grounding is an excellent source of information. At around $50.00, it’s a great investment that can really help clear the fog surrounding grounding and bonding in the NEC.