I'm not going to do the detailed testing you do but since I've used both the batteries: the Anker 2nd Gen Astro E5 16000mAh Portable External Battery works even better for my use. It is physically larger but doesn't heat up when charging and the charging rate seems to be quicker (higher mW).One battery pack that worked:
Anker 2nd Gen Astro3 12800mAh 3-Port 4A Portable Charger External Battery Power Bank with PowerIQ
http://www.amazon.com/gp/product/B00CEZBKTO/ Review coming... with minor caveats.
http://www.amazon.com/Anker-16000mA...=8-1&keywords=Anker+2nd+Gen+Astro+E5+16000mAh