OK, shame on me. Apparently I am not able to describe my original issue well enough for anyone to understand or I put too much distracting other stuff in my description. I will try again:
I understand that my previous screenshots may have contained a lot of stuff that suggested that there might also have been tiggering issues. If triggering on an inactive channel might cause issues with data acquisition, I will prevent doing that that in the future. However, since the tiggering is not related to my original issue, it would be nice if we could, for now, ignore all triggering related matters altogether.
Regarding the Horizontal Reference Position, you mentioned: mine is set to a "Delay 50%" and works exactly as intended when the issue does not occur. If I change it to "Position", it also works as intended, when the issue does not occur.
For reproducing the issue, lets assume that I have recorded a data burst with the memory depth set to 200Mpts and the timebase set to 200 ms/div while not in stop mode. Lets further assume that the trigger was set to D3, armed in single shot mode, caught the correct rising edge and we now have a perfectly fine recorded waveform and the scope is in stop mode again. This state can be seen in following screenshot.

Now in this state, I change the horizontal position to the end of the data burst (which is then in the center of the screen at my set reference position), and then change the timebase from 200 ms/div to 50 ms/div to zoom in a little on the end of the data burst. While changing the timebase, the scope correctly zooms into the position, I defined as reference position (Delay 50% = horizontal center of the screen). Now, if I do one more step to 20 ms/div, the scope does not stay at the correct position, but jumps to somewhere at the beginning of the data burst. If I go to 50 ms/div again it returns to the correct position. While all the changes of the timebase value, the offset of the reference position, displayed at the bottom of the screen stays the same. So obviously, the scope is displaying data at a different position than it pretends to do. Exactly this issue can also be seen if I activate zoom mode at the same position with the timebase set to 50 ms/div or above. To prove this, I have made screenshot in zoom mode that clearly shows that the potion of data shown in the main view and the highlighted potion of data in the overview bar at the top are not the same, although they should be.

So as I see it, my scope cannot access recorded data correctly when the memory depth was set to 200Mpts. Any attempt to display the recorded data at a certain smaller timebase value and below will lead to an incorrect potion of the data to be displayed. It does not matter if this condition is produced by simply lowering the timebase value or activating zoom mode.
I hope this attempt at an explanation was easier to understand.