I just thought I would post this here if it could be helpful to anyone else.
According to the manufacturer website @Pharma provided (thanks again!), the amino acid surfactants Sodium Cocoyl Glutamate and Sodium Cocoyl Glycinate are both considered to be quite mild.
However, the Glutamate ones are described by them as “moisturizing, mild, and soft” as well as “hypoallergenic.” While the Glycinate ones are described as “leaving the skin feeling ‘fresh’ without leaving it taut” and as having “high foaming properties.”
So I would say that based on the descriptions by one of the pioneers and major manufacturers of these surfactants, the Glutamate would probably be most ideal for anyone seeking the mildest option.