off hand, I'm not sure the tip size. but it is a very common size. if you take your HD-P2 to radio shack, I'm sure that you'll be able to find one that fits nicely. I know, not much help, but that's my suggestion.
also, the 8000mAH battery should be great for you. I power mine with an external 4200mAH NiMH battery. that does me quite nicely for opener + 2 full sets of music, and I don't think I've really come close to draining it all the way. with 8000 mAH, you'd be golden.
the 600mAH is what the manual says, but I think that that is more of a "max draw".
I see that you are running e MiniMe in front, so I assume you are going S/PDIF. based on my rough calculations, with the backlight OFF, and running S/PDIF in (i.e. not using the HD-P2 phantom power, internal pre-amp, nor the internal A/D), I think the current draw is roughly 450 mA.
therefore 8000 mAH / 450 aH = 17.78 X 0.8 = 14.2 hours.
I think that's a reasonable expectation when running S/PDIF.