Remixed from the original, which fit the rack great (even without zip ties), but was a little tall, and I thought the screw on bottom issue could be solved. You'll need supports under the part that attaches to the rack (which I included in my attached Code print file.)
I included 2 separate design files. One looks like the cup holder is covered by a giant block, but this is an exclusionary support block modifier that will disappear when sliced. The other design file is just the cup without any supports or modifiers (you'll need supports under the part that attaches to the shelf.). I also included the Gcode with the correct supports to make it as easy as possible.
If you have any questions, don't hesitate to ask.
The author remixed this model.