The worst of all options is to fly WAS-JFK on a separate ticket. Not only must you allow sufficient time to reclaim your bag at JFK and meet the SQ check-in / bag drop deadline, but the risk of a no show falls on you. If you are sufficiently delayed into JFK and no show for SQ, your ticket will be cancelled and will retain whatever value it has under its fare rules, most likely $0. This means having to purchase a new ticket at walk-up prices. The micro-hauls on that route are often delayed or cancelled when there is the slighest hint of weather and you must account for that too.

As you are in Washington, it makes sense to take Amtrak WAS-NYP. There is a train pretty much every 30 minutes, alternating between Acela (F & J) & NE Regional. From NYP you can either take public transportation or an Uber and be relatively assured of maintaining schedule.