The most obvious solution is to keep the TXL-AMS leg and find something on DL metal from AMS to the US and on in to NYC. I'm surprised AMS-JFK wasn't offered up right away. Skipping LHR will save you the UK APD, too. Alternatively, try AF to CDG and then back to the US.
Alternatively, in addition to the FRA, MUC, etc. options already suggested, see if anything is open on PRG-JFK. The train ride isn't that long.