A FlyerTalk Posting Legend
Join Date: Sep 2009
Location: Minneapolis: DL DM charter 2.3MM
Programs: A3*Gold, SPG Plat, HyattDiamond, MarriottPP, LHW exAccess, ICI, Raffles Amb, NW PE MM, TWA Gold MM
Posts: 100,413
Don't try to do this by chat: it's outsourced and folks here have been complaining about the agents.
Normally with a cancellation, DL permits you to rebook plus or minus one day, although the automatic system tends to put you onto the next available flight. Try to search for flights yourself first before calling DL so that you can ask for the flight numbers (be sure to be clear about times and dates) you want.
Assuming that this is on one ticket/PNR, rebooking to a BOS nonstop should be allowed, assuming that your "NE" destination is within about 300 miles of BOS, although you'll be responsible to arrange and pay for your own ground transportation. (I'm guessing that there's no connecting flight from BOS to the NE destination; if there is, certainly you should be allowed to rebook to another legal routing.)
If you paid for D1 on LAX-JFK, you might be able to get a refund.
BTW, is there a decent routing through LGA instead of JFK, although this is likely to require two rather than one connection due to the perimeter rule.