Probably a ground loop issue here?
How many ground wires go to the flight controller? It should be only one ground wire! ESCs / servos should have only their signal wires connected to the FC. Then there shouldn't be invalid voltage readings, regardless of current being drawn.
BTW, connecting together the +5V coming from BECs built in the ESCs is a key to disaster
Voltage sources shouldn't be wired in parallel. There are always minor differences in BEC voltages that may float with temperature and once the difference is big enough this will stress too much one of the BECs, causing more and more current to be drawn from one BEC to another in attempt to equilise the voltages, this will heat the BEC even further, causing bigger drift in its output voltage, etc... Finally the BEC temperature rises so much that it causes the ESC to enter thermal protection mode and the quad, presumably, to crash...
Shunt type current sensors we commonly use are not precise for small currents, I prefer calibrating them for typical in-flight currents (8-15A, for example). The easy and precise way is using a current/Ah meter, compare its readings to what the GCS reports for mAh used (via Oplink telemetry) and correct the calibration coefficient respetively.
Zero current trim should not be used with this type of sensors, it makes sense and is intended for hall effect current sensors (like ACS758LCB-100B).
To have best calibration results, telemetry should be via Oplink, and no USB cable connected.
https://rcecho.com/skyrc-rc-model-wm-010-high-precision-rc-hobby-battery-watt-meter-bk210/