I got confirmation on Wednesday, that my interpretation of the Parks Department and Mayor's Office of Film, Theater and Broadcasting regulations, that tripods may be used without a permit in all city parks, was correct. So, I'll be able to continue in filming in Washington Square Park.
I am still concerned about the ambiguity of the Parks Department's regulations and their website pages surounding photography. Every photographer I know with a large telephoto lens has been hassled at least once by a Parks Department employee without cause. I have to decide if I want to collect enough documentation to prove that what I experienced last Sunday was the norm for photographers in city parks, and pursue the matter futher.
But for now the good news is that I'm safe to photograph Rosie and Bobby in the park again.