I remember reading an article about a Falcon 20 with an autothrottle which was biased to hold optimum AoA. Apparently, the folks got an impressive fuel economy flying a sortie from the US East cost to the West coast which would not have been possible otherwise. I would think as the airplane got lighter speed must have decreased since they were strictly flying an AoA. I reckon fuel economy would have been even better if they had step climbed as well.
Since normal operations are usually flown at a constant Mach number, AoA will change since the airplane gets lighter. Looking at the long range cruise numbers in my AFM, speed will be higher for higher weights and lower for lower weights. There is one best range/long range Mach number for a specific weight.
Not exactly sure what a particular FMS presents as max range speed. However, I think it would not be unreasonable that it presents an 'average' best speed for a particular sector flown. Just my guess.