My great grandfather was also EHC. His grandmother was Clara Olive Whitehead and her father is Charles Whitehead of Bristol RI. Not sure if they're Native American or not and I'm not even positive that I traced everything accurately, but that's what I have. Clara seems to be a family name, just like Edward, so I think it's right.
I too have been curious about the Native American roots. Let me know if you find anything.
My mom, Marlene was EHC's granddaughter and one of the 3 daughters of his son, Edward. Her brother Edward died in 1980, right before I was born.