My longest is 32676 miles: hkg-yvr-jfk-yvr-dfw-anc-dfw-ord-lax-lhr-cai-lhr-hel in a mix of J and F with the only breaks of more than 4 hours being in YVR and the overnight turnround in CAI where I simply stayed in the departure hall. Trip report in 3 parts here:
http://www.flyertalk.com/forum/showthread.php?t=181877
http://www.flyertalk.com/forum/showthread.php?t=181886
http://www.flyertalk.com/forum/showthread.php?t=181899