Ok, I solved it in a way that I'm thinking "why didn't I think of that before?".
Since I'm on the west side of Boston and I have to be about an hour east of Syracuse, it takes 5 hours to drive. And since I have a rental car already, I might as well change the drop-off location of the car and just drive there. From door to door going by plane would take about 8 to 9 hours so I might as well drive

So I only had to change the ticket that I'm only doing one segment, from SYR to JFK, and that change costed me only 6 dollars

@Pete838: It depends on the mood of the agent at the check-in counter. If he/she is in a bad mood, they can just label it all the way through, they don't HAVE to short check it.

Thanks for all the replies!