Jim please post your program as I can't find the ap note you referenced.
I am facing similar situation. So, have you solved with the problem, Jim?
No but now I have adapted the code from AN92584 and it is better ~0.200 µamps.
I did some measurements too using 2 methods, one described by you and another by simply using a digital ammeter in series with J15. Of course the second method will average the current and more precised measurements should be done with you method!
I can confirm your findings but to be honest a spike of 50 mA is why to much. I have about 193-200 mV using a resistor of 20 Ohms and a clock frequency of 32 MHz, which is about 10 mA. I also suppose that with a clock at 48 MHz( if this is also intended by you to use) the spike will note overcome 14-15 mA, since the clock for BLE is at 24 MHz.
I also used other lets call them benchmarks, where I have analyzed the power consumed by executing only asm code removing all other components for a design, and also using simple BLE application just for advertising, sending, notification, keeping the connected link etc. using the same Application Note AN92584 and after my results on a simple project I can tell you that with a 250 mAh you will have the battery for about 4 days, if my measurements are correct. I still have to test more the system and to remove more unused clocks and other parts in order to obtain better results.
Hopefully this helps.
So you just used the code from that appnote, but the measurement procedure is still the same? using oscilloscope?