767-300 at .80 fuel flow increases 5%-8% if you're 4000' too low(boxed data so it's not perfect, ergo the % range).
ISA deviation from STD is 3% for/less (hotter/colder) for every 10C.
So to get better fuel efficiency 4000' below OPT ALT you'd have to have a temperature deviation of approx. 20+ from the lower altitude - ie FL 310 ISA -10C, FL350 ISA +10 C.
That's a very rare occurance.
Jet engines fuel consumption is like a wind up toy, they're only going to last X long no matter what you do.
If you wanted to get max endurance you'd take off and climb at slow speed to the mid 20's at holding speed. Endurance would be increased about 10% over an efficient cruise speed.
Range will be significantly reduced to perhaps 50% of what you'd achieve at an efficient cruise speed.