I saw the problem you told us; I also saw that if I add some more lines to the control, when I click on it it automatically opens a popup window to select an item on it. It's not one of the standard CVI popup windows and I don't know how to call it instead of the drop-down menu: maybe NI people can help you if this way you can manage your problem.
A workaround to limit this problem is to transform the ring control into two controls: a string indicator and a popup menu ring (the button with the down arrow only): putting the popup menu ring on the left of the string control can help you, since you can arrange the ring position so that the drop down menu remains visible. Once the user selects an item from the list, you can update the string indicator
to display the text of the item selected.
I attach a modified version of your UIR to show this solution.
Hope this helps
Roberto