Capn Bloggs; "the IAS for max range changes (reduces) as the weight reduces to maintain the best L/D"
It is dangerous to use the terms "max range" and "best L/D" in the same sentence. A jet at an IAS for max range is not at the speed for best L/D.
Generally, for a jet, flight at best L/D gives max endurance (usually close to published holding speeds) and is at or near a constant aoa.
If we want best range however, we need to fly at the speed where the ratio of TAS/FuelFlow is the greatest. This is faster than the speed for best L/D, and is not at a constant aoa.
Best L/D speed is the lowest point in the Thrust Required vs TAS graph.
Best range speed can be determined by drawing a line from the origin to the point where it tangents the Thrust Required vs TAS graph. Some assumptions of course, eg constant TSFC Thrust specific fuel consumption (lbs of thrust, per pound of fuel, per hour)