Hi all! I would like to thank you all once more for your ideas. I finally was able to get this think apart. That screw really looks like something not originally being added by CDI. I can see its function in preventing the spindle to move upwards, but that is supposed to be taken care of by the bolt through the upper part of the spindle as well as the extrusion.
Long story short: I was able to remove it, and then everything came apart like a charm. I disassembled the turnbuckle, added a washer and put the thing back together. Rolls like I was hoping it would.
One difference to the original configuration remains: It seems, there should be a washer ON TOP of the white plastic, but it has to be larger than 1 1/2 in diameter and smaller than 1 3/4. I measured the boring with a caliper , and it is some 1.7 in, so just short of 1 3/4. A 1 3/4 washer wouldn't fit in, and a 1 1/2 would slide all the way in, not giving the plastic part any support. What I ended up doing was putting a smaller washer BELOW the plastic piece, i.e. between the cup and the white piece. It does the job increasing the distance from the cup's bottom to the spindle.
No idea how that custom screw got there, but I put it back in, since my washer is now below the assembly anyway.
I'm hoping to have the mast up next weekend, and then I'll let you know how this fix works in "real life"

Thank you all!
Mario