Have you checked the NJ Historical Society files on the Phillips family yet?
http://www.jerseyhistory.org/arch_browse-family.html I do not know what it will yield, but given this family's ties to the Demarests it might be a fun adventure. Also, please consider trying the spelling Fillips for this particular group. NJHS has files for that spelling, but under Phillips.
Finally, I do not know if it will yield you parents but it may well yield you some cousins. http://www.phillipsdnaproject.com/ylineage/pedigrees-by-family-group/128-main-list-lineages-1-to-50 Look at family group # 35, which specifically pertains to your Matthew and Mary and offspring.