I was using off-grid in the most straightforward of senses - off the electricity grid. That doesn't necessary mean stationary or without weight limits (as solar would require) - it could mean long distance trucking, or logging, construction, or even the maintenance of electricity pylons (which probably can't be turned on during that process).

All those require huge amounts of energy, and batteries are not yet nearly there (as others point out, your numbers for battery energy density are out by a factor of 30).