I've found the resolution to this issue. To define the up direction for the animation, you need to use the bounding box and then regenerate the path for the camera.
1) Move the region (aka bounding box) until it's bottom is where you'd like to define the plane of the ground.
2) Run Coordinate System to Bounding Box (found at
http://wiki.agisoft.com/wiki/Python). This will adjust the internal coordinate system to match the bounding box.
2a) This can be done by saving the script as a .txt file and modifying the file extension from .txt to .py. The script can then be run via Run Script in the Tools menu.
3) Generate a new path for the camera. If you omit this step, the path for the camera will continue to use the coordinate system from before step 2.