If you make the top part (that goes into the spaceship or whatever) without treads but with a tight fitting bushing made of synthetic rubber (like urethane), or make the entire top part in urethane and then keep the rod without the treads (but with a few mm of taper to ease insertion).
This way you will be able to get a friction fit that can be turned in any direction and still hold its position. It will be much cheaper to make as well.
Another option would be a bushing on the flat part of the stand and this will ensure a longer life, as 3..5mm acrylics are bound to chip and crack, sooner or
later even sooner, from tension, when you repeatedly tension a screw into it.