G'day Geardoor
I believe the way to achieve absolute maximum range for a given quantity of fuel is to continuously climb (obviously not always possible in a practical sense). The two considerations are the airframe and the engines.
Firstly for the airframe to be operated most efficiently it must be flown at the optimum AoA which will require the speed to be reduced as fuel is burnt.
Secondly the engines need to be operated at their 'design point' which is their most efficient regime. A continuous climb allows the engines to remain at the constant, most efficient RPM.
Beware: possibly completely untrue.