How can I stitch a panorama with a smooth horizon when shooting from multiple handheld positions?

It's hard to tell, but it looks like in the stitched image your camera might have been aimed slightly above the horizon in at least 2 of the unstitched shots. By aiming up a little bit, the horizon at the widest part of your image "curls upwards" somewhat. This effect is similar to barrel distortion, and is more prominent with wider fields of view (shorter focal length lenses).

The solution is two-fold:

1. Make sure your camera is absolutely level to the horizon. Use a bubble/spirit level on your tripod to determine this. In this case, it's the up/down tilt axis that is the most critical, that you're trying to resolve.

2. Stitch together more shots, rather than fewer. The problem you want to avoid is distortion at the edges of the field of view. So increase the overlap for each successive shot (i.e., don't rotate as much between each shot, taking more shots). One way to do this is to rotate your camera to portrait orientation, and take your shots. You will be using the short axis of your sensor frame, thus requiring more shots to cover the same final stitched field of view as you would if used your camera in landscape orientation.