I did some more testing without a load but with a beefy power supply in constant current mode (the source be the load!) now. 6.4A through the 0.05 Ohm shunt is working beautifully for extended periods of time. The shunt gets to 82degC, so some active cooling with forced air is probably on order.

Here is a plot of test results, that show tolerances <2% across the range. Measurements below 200 uA are getting inaccurate. In general, tolerance increases at the lower end of every range, which means more noise at lower voltages across the current shunt. 

More numbers and graphs to follow. And I need a different load to bridge the gap between 60 and 100 mA.