If you're not open to the capacitor source test, then insert an ammeter in place of one or both of the shunts (red to the positive side). Set on "DC milliamps" the meter should average the current and will indicate either + or - current and you will then know without the need for any fancy equipment. If the meter stays on the - side, then indeed a net current is going into the battery.
Next I would like to draw the readers attention to Harvey's 'Techno-Babble' #2523 where I state:
It is currently the only conventional answer to this problem I see so far and I think we must allow ourselves latitude in the part values to accommodate the claimed result.

I was surprised that my simulator produced waveforms very similar to the aperiodic actions we have seen when the HEXFET current was pushed to its limits. Well, more on all that later - I am still busy tasking 3 projects at once including this - but I am so interested with this it occupies most of my thoughts. In the recesses, I know that the measuring technique of subtracting power during the negative excursions was an error for Ainslie's group, but consciously the energy content contained in that portion seems much too small to account for the total values even though that is a compounded error in that it adds to the heat but was subtracted from the current sensing readings. Still at it.

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