Sorry I did misread. In any case yeah I wouldn't be too optimistic about it working. But, there is also the second daily FRA-SIN flight, so if you can find a date with JFK-FRA availability alone then you do have more options for the second leg to connect that to (though only in First, not Suites, if that's a dealbreaker for you). But I have not found JFK-FRA alone all that easy to come by, either, except sometimes for last-minute bookings.