Bob,
I don't know for sure, but I think it is just using the unloaded voltage to calibrate the % remaining. For this it uses some standard Lipo curve relating capacity remaining vs unloaded pack voltage. So if the actual lipo volts vs capacity curve has changed a bit over time (as the manufacturers make subtle changes in the battery itself, this "gas gauge" may be slightly off, especially when you are down in the lower ranges.
I see sort of the same thing as you. The initial calculation when I plug it in is in the 20-24% range, but if I look a while, it drops. I am not sure what is going on here, except maybe the charger is actually doing a little discharge as it tries to figure out the cell capacity (to calculate the current it wants to put back in at a 1 or 2 C charge rate. However I am not sure at all about this. I basically just look at what it puts back (70-75%) in and compare that the first value--and it isn't that far off.
One thing to remember is that the pack capacity you know is what the manufacturer claims when they make it. That capacity begins to drop off as a function of age and our "abuse". For example when we calculate that 70% being put back in, we make the calculation by dividing the mAHr put back in by the original capacity. That tends to underestimate how much we have taken out (% wise) of the older and used pack. So what I am saying is that your original 2600 mAHr pack might now be a 2400 mAHr pack.
As regards to the voltage under load, the only way to get that would be to put a data logger on the plane as it is flying. Then you can see what the pack is supplying under "real" conditions.
The other way is to put on a wattmeter and simulate the power loads. It is a bit tricky for an event like carrier where you really pour the coals on at the beginning, and then go into slow flight, with occasion bursts of power. So you could try what you suggest--blip the power with a watt meter attached after a typical flight.