If you are looking for a paid cash ticket in business on those routes, no one can give you any secrets other than Kayak.com and keeping your eyes open for sales.
But one way paid business class on these routes are never going to be cheap. The cheapest on FRA-JFK will likely be on Icelandair via KEF or Aer Lingus via DUB. Singapore is often competitive on the nonstop FRA-JFK. But these will all show up on kayak or Expedia...