Bat-try

You can, of course, get the Tascam DR680 modified. Busman audio does modifications -- 6 channels for $300.

The Tascam DR680 is fairly small and light.

I need a decent way to remotely power the thing. One could buy these Chinese 12v batteries (apparently the charge time on them is long though).
Or if one wanted to go rechargable and AA there are these Eneloop XX batteries.


Or you could go crazy and get a 12-pack of Energizer Lithiums for the whole shoot. Lessee, if, and only if, you could do an 8-day shoot on only 4 12-packs, that's about eighty some odd bucks.
 
So the conclusion is: ah. Erm.
There's also the option of getting one of these high capacity batteries for DVD players. That's $200. Word on the street is that it works.