HX711 Load Cell application strange behaviour
1) Put your power source on an oscilloscope and check it. I assume what's happening is you don't have a clean sine, and the power fluctuates, whereas power from a PC USB port is usually very well regulated. This may be causing issues in your sensor due to under/over voltage at a minuscule level.

2) Because you're pushing your sensors to the edge of their capabilities, you're going to have to work around them, so the normal scenario's don't really offer much help, as they are usually based on working within the middle ground of capabilities. 

You said that factoring based on low load vs high load created unreliable  variances in your measurements, i would personally suggest calibrating not for max load, nor min load, but 2/3 of max, or 1/3 max, and see if that stabilizes you, or at least gets you somewhere to the middle of the road where your differences are nominal, or something you can live with.