Currently, Spine approximates the export image size based on the bounds of the poses of the animation. So between animations, the pivot points are likely not aligned.
The current workaround is to add a rectangle image behind your skeleton to force Spine to use it for the bounds calculation for all animations regardless of poses. You just have to make sure none of the poses go beyond that rectangle. Then make that rectangle transparent by changing its attachment or slot color, so that it's not visible on the exported frames themselves.
Exporting individual frames for Unity to pack is probably better than a prepacked sprite sheet. Unity's tight packing is better at saving sprite atlas space than than any grid packing.