i did some testing with the 9 volt walmart type lithium ion battery and the hdp2.
i ran 24/48 spdif from a v-3 and got 11 hours 29 minutes of run time.
i ran 24/48 analog in phantom power on and got 7 hours 49 minutes of run time.
so it appears that the hdp2 will work just fine with a 9 volt lithium ion battery!
Manual mentions "RASH Current" of 600 mA.
5400 mAh (the capacity of my walmart battery)/600 mA = 9 hours of run time, or as you tested 7.8 hours of power...
Guess "RASH" means analog-in with phantom???
The 9V seems to work with my HD-P2, though I have yet to tape with it. I made up power-cables today... I can always run my 12c SLA if I have to...
Terry