Hi again, sorry for long delay.
I'm an ex-graphics programmer - so I can help with this some more.
1 - the mouse? cmon
this made me laugh
2 - it's not z fighting, I know what that looks like.
3 - I'm running Win10x64 Pro, Ryzen7 1700X cpu, and two Radeon R7 260X gpu's in Crossfire( gpu driver is 19.3.3, only a few months old).
4 - I've attached 3 screenshots, so you can see exactly what it looks like.
Setup of screenshots - made Body1's cylinder, made Body2 and started making it's Shapebinder.
A - Have clicked the Task's Object button, but have not clicked the cylinder yet. Note the camera controls top right are fine.
B - Now I've clicked the flat end of the cylinder. Note Object button deselects and "Pad" is added to the field. Also note the camera controls are gone.
C - I've now shift+rightclick rotated the view downward a bit: see how the visual is corrupted.
Taking an educated guess: that looks like an invisible copy of the cylinder's orientation in B is clipping away the visible model. Either a real copy is there only drawing into depth buffer, or the depth buffer stopped updating (keeping a depth-hull of the B orientation).
Hopefully this helps you reproduce!