Wow, that power meter is serious, pretty good for an amateur!
This graph of a rectifier power supply sums it up:
The mooshimeter is certainly as capable, it just needs a new mode, similar to the AC voltage mode, where it does the multiplication before the averaging. Probably more work to get the app right, than the meter.
Oh one more thing, in logging mode, it would have to integrate the total energy in each logging period, then divide by time to get the true average power over that period. So logging of power would require continuous sampling and processing, which would affect the battery life a bit. I suppose the same could be done for V and I, average over the period instead of discrete samples.
True Power measurement was a feature promoted with the launch, it would be great to have it working!