I had a TCD-D7 for about ten years until it died last september because of mechanical problems.
I used ist mainly for recording film sound.
I powered it with a 6V Lead Acid Battery with 3.5 Ah and that was absolutely reliable. The battery was about as big as the D7 itself but it became never ever empty and I could record a whole day long!
Disadvantage: The DAT "thinks" that there's an external AC adaptor plugged in so it doesn't go into power save mode and the battery level isn't displayed. Maybe you can modify your D8 so that the external power can be connected through to the AA battery hole in the back - then this won't happen.
Cost: Lead Acid Battery (Panasonic) about 20 Euros in germany (25 Dollars) and a fitting charger about the same price.