How to track video where markers pass behind foreground object

I need to track video where there is a tall object in the middle of the scene. The object in my scene would be tall enough to span over the horizon on the top. This mean all my tracking points are on the ground. This causes all my tracks to eventually pass behind the object in the middle making it impossible to get 8 solid tracks all the way through the video. My objective here would be to track additional objects on to the box… like another box on top of the box in the video.
Example footage i am working with:

The only difference is in the real video the top of the box will be too tall to be in frame, and the cameras path will take it an a full 360deg path around the box.

making it impossible to get 8 solid tracks all the way through the video
You don’t need 8 tracks for the whole sequence, only between the two keyframes that you set in the Solve options

Choose tracking points at key positions in key frames. If the motion of the camera and the object are steady throughout the shot, the outcome will be believable without too much computation.

Make it as easy on yourself as possible. For instance, in the gif you showed, “put the camera on a truck.” (A used baby-carriage makes a fine truck. So does an old shopping cart.) In your example, the object jiggles-around in every frame, to a distracting degree, and that demands that every frame be laboriously computed. If you don’t have a real steady-cam … in-camera image stabilization really doesn’t count … build a truck.

Or a boom … a long piece of PVC pipe clamped to a tripod with a bunch of sand-bags holding it down. Shoot, move the rig somewhere else, shoot again, stitch it all together later.