Here is your file back, Lopolo.
Scene file
https://www.amazon.com/clouddrive/share/f5BWRVr3zBEjGfdzAgegV65zhVk2bnu6JhgRPBciiVX
This is not perfect since I added only a few extra trackers to it. The plane.1, has already some manual adjustment on the f-curve, to follow more the quick movements of the target, but it is indeed not even close.
My suggestion:
Pre-roll, give the flat target more perspective for the camera, slowly to the right, to the left and if possible backward, so the X marks on the white rectangle move through space. Even move closer to the camera for a moment might support the solve.
Use a stronger cardboard, if I’m not mistaken the frames around 190 shows it more bend than before and after.
The best would be of course to stick a little box in the middle of, or perhaps a pyramid in the middle, so the tip of that object would be much closer to the camera and in this way produce better spatial information.
Make a lens profile, the smaller the tracking area, the more any tiny little bit of lens distortion counts. In this case even more, as it is more a planar tracking than a spatial. Take the lens profile in the distance you like to track. Or at least set the focus to that distance. Lenses as you undoubtedly know, breath, so the wrong length will lead to weak results.
Never believe what is written on a lens. (Except it was hand calibrated (Master Prime, etc.). I assume you have a Canon EF 24-70 lens in use (Or Sigma… etc.), which one from that series alone will change the outcome already, as they never give you exact 70mm on the longer end.
Track each of your marks, the more data, the better in this case. There are parts with a lot of motion blur, take especially good care of those.
Typically people suggest measuring from the sensor, (the O with the | in it). If you are close and want to be precise, use the nodal point of the lens in the final measuring. A 70mm on a 24.6 sensor has roughly a 20º field of view, that is relatively long (I do not mention the equivalent measure, as that is nonsense, sensor are cropped, not lenses). While being already on the longer end of the optics, the smaller parallax given is even more limited. Hence my tips to get more data.
Since the scene is measured, so I assume, the tracking rectangle should be used in the exact same size in the scene. I have used an old trick from Tim Dobbert’s book here, to have a polygon (not a primitive!) as a child on a Null. The Null is located on the upper left corner of the plane, precisely on the first point so to say. That allows to quickly position the plane into the scene. All adjustments are made with the Null only: Position it, then rotate it.
Yes, Mocha came to my mind as well, since we’re are here trying the C4D route… Triangulate the camera position perhaps.
As a side note, I wouldn’t use only an X on that target, as they are all too similar, and it takes more time to adjust. Use other signs as well.
BTW.: I created in one exploration also a traveling mask, which allowed me to automatically produce only trackers inside of the target. But the result was not so much better than the manual trackers in the scene above.
All in all, the scene above shows that a result is possible and I hope that by using all X marks on the target, while added my suggestions to the mix, that a result is very likely achievable. If you bake that plane, minor adjustments can be made, e.g., deleting noticeable single frame spikes, or at least lower those.
My best wishes for your project