Lateral thinking strikes again - maybe

Having discovered that the Port Authority of New York and New Jersey - which is responsible for the New York airports, it seems, as they run the websites for JFK and Newark - runs a decent website, my next port of call for finding decent air fares in the US - seemingly impossible as all the websites are shit - is tracking down all the companies that fly to JFK, and getting in touch with *them*. No idea whether it will work yet, as I haven't found out whether any of them are actual budget airlines, as opposed to the majors who all charge the same prices.