Interesting read bbunks. A full passenger load on a 6:45 sector however sounds interesting, how are your -800s configured? We flew once a 2800NM sector (MUC-SHJ) and had to restrict our passenger load to 160 pax and no cargo in order to always make it without a fuel stop. On our common 2000NM trips however we can carry full loads including cargo.
@blackswan: the 737 NG is ETOPS capable in its basic configuration (in fact you have to pay extra for example to get a non ETOPS low fuel warning), however you need to observe some additional maintenance and operational procedures.