Actually, you should measure your amp driving your phones from your sources. I did, and it was only drawing 30 mA. That makes the battery situation much more workable.
Each AA battery is 2850 mAh; since you have 16 in series, you might actually have a prayer of drawing them all down to their lowest usable voltage before the OBH-11 craps out. So let's blue-sky it: 16 * 2850 is 45600 mAh. If you also get 30 mA of drain, they'll take 1520 hours to tap out, which will take about 2 months if you leave the amp on 24/7.
Now, those numbers may not hold up in real life. But they sure are encouraging, no?
Now as for 9V, the extra voltage shouldn't hurt, but I would be prepared to replace the amp if you fry it -- this is outside the spec, after all. But, there is a regulator inside the OBH-11, so there shouldn't be any trouble.
A single 9V is 600 mAh. Three would be drained in only 60 hours -- a factor of 24 difference in run time! So what do you value more: run time or portability?
As for rechargeable 9 volters, most of those are only about 100 mAh -- check the specs. Therefore, you'll be recharging often. Seriously consider using 6 batteries: two groups of in-series batteries paralleled. Since current drain and voltage will remain constant, run time will go up.
FWIW, there have been a few threads on this topic recently here on head-fi and on headwize.com as well. You should read those old threads as well.
