This may sound crazy, but what if you put a very low value resistor in series with the supply to the Vcc pin, like one ohm or less, even a stretch of thin wire, and then hook up your oscilloscope to measure the voltage drop across that resistor. With some math, that would give you the current. That would need to be your floating scope, not referenced to ground, or perhaps measuring 2-channel differential voltage. If you could get that to work, it would give you a full picture of not only how the sleep and active currents compare, but the duty cycles as well.
I've done this on what I assume would be much higher currents than you're looking at, so it may not work for you. And the scope leads might interfere with the processor or otherwise swamp the measurement. But if you can make it work, you can see exactly what's going on.