Now I see that the OP wrote about spring. Where do you see that he is going to DC?

This trip is in May and Yes I am an American Citizen and realize it will be a close call. I do have a plan B of an 8 AM flight out of JFK on Wednesday but really hoping I can make the 10:05 PM train my flight gets in on Cathay Pacific at 8:30 PM. Not sure how often the flight gets in early/on time. I think its doable to make if I am out of the airport with my luggage at the latest 9:15 PM.

I'm actually going to choose the other approach. The taxi queue might have you waiting at JFK instead of moving unless you reserved a car.

I think taking LIRR is your best bet!
LIRR is 20 minutes into Penn Station (you don't have to worry about traffic or possible event at MSG) or possible traffic. You are in the station and just need to find Amtrak departure track. So based on current LIRR schedule there is a 9:33pm departure from Jamaica which arrives into Penn Station at 9:55pm - perfect if you already have your Amtrak ticket.

I have driven from Manhattan to JFK and most of the time is cross-town (Midtown tunnel to West Side) and stretch from JFK to LIE on Van Wyck/GCP.

The factors you can't control at JFK airport:
Your plane may land on time but can't make it to gate ontime due to other airport traffic
You may get stuck at customs due to queue of other flights arriving ahead of yours (not sure which airline or terminal you are arriving).
As 1st class your bag has priority to arrive at belts but we are talking JFK which doesn't have the efficiency of other airports.

To your advantage - most airlines allow extra cushion time so probably would arrive earlier than anticipated. I suggest you check the flight status daily to see the actual arrival vs. predicted arrival to see the opportunity.