Camera Orientation

The camera's field of view is approximately 35°x50° (34.9°x50.7°, actually)

To try and have a panorama that is as “deep” as possible we will mount the camera in a vertical (portrait) orientation tilt it downwards

We must also take into account the horizon dip caused by the high altitude, i.e. the fact that the horizon is lower that 0°, as we are high enough to start seeing a round earth. From the formula:
                dip= √ ( 2 * altitude / Earth_radius) 
(taken from this page) we have the following values:

Altitude  Dip
10 km 3,20°
20 km 4,53°
30 km 5,55°

We will assume a 5° dip for the horizon as a good approximation. If we keep the camera level, the 50° FOV would be (on average) pointed as follows:

The red mark signals the actual position of the horizon, about -5°.

I propose to tilt the camera down by 25°, so that the upper side of the frame is horizontal, like in the following figure.

It is clear that in this case we have some risk of having the horizon cut off, especially if the camera swings a bit. If the oscillations are small, the coverage is still good. The following diagram assumes oscillations of +/- 5°:

Practically all images still capture the horizon.

If the oscillations grow, we will have some photos that do not capture the horizon. Assuming oscillations of +/- 10° (which I think is the approximate values in high altitude) the coverage we will have is the following:

We should still have more than 50% of the images that include the horizon. Even with stronger oscillation, the same holds true: at least 50% of the shots should enclose the horizon.