I just wanted to drop in here and inform you that the original 640mah battery for the sony hdr-az1 camera will fit in the edge 820 with the plastic casings removed.
There is an 800mah battery available online aswell, i have yet to try that, but i would assume it's a bit thick so you would likely struggle to make the cirquitboard to fit in the casing.
I have now recorded 5 hours with no powersaving features connected to phone wifi and HR strap and brightness at 100% allways on.
I still have 24% left.