Current Monitoring circuit setup and option exploration for IoT device testing
You run out of dynamic range too easily, there is a reason this is a hard problem to solve.

Lets say you use a transimpedance amplifier to measure your currents, this way there is no voltage drop to affect your reading, and you get a direct voltage output (would need other supporting components to be able to sink 200mA, but this is to show the issue)

lets say you scale things so 200mA = 5V, and 0 = 0V, 1uA then ends up as 250uV, which while measurable needs quite a lot of effort as your at 18 effective bits of resolution minimum, to get nanoamps your at 28 bits, this gets even harder again as you start hitting against noise limits, as you probably want to sample these currents at KHz - MHz 

TLDR, your in the ballpark of 5.5-7.5 digit DAQ/multimeters, its not easy or cheap. and just because that audio ADC says its 24 bit, does not mean the result is accurate past the first 14,