I'm the keeper of the tree with Parks on it and my gGrandmother was a Parks. I am a 5th cousin 4 times removed with Moses (whatever that means)
There is a book on the Parks that I got most of the old information from and I will look at it later to see if there is any mention of a family crest or information about Robert being a knight.
It's interesting that Moses' Mother was called Thankful too, I would have thought one thankful in the family would be enough.
The Parks have two towns named after them: Parksville, NY and Parkston, NY