Single-Select uitable Cells

I have a simple GUI that displays a whole bunch of characters (the result of cellstr(char((0:10000)'))). The idea is that when I want to print a special character I want to launch this tool and select the character I want and have it display it's code at the bottom. I then want to make use of that code to convert to a char so I can print it.

The problem I'm running into is that I'm using uitable and I cannot find a way to enforce single-selection for the table. I wrote a fancy algorithm, for the CellSelectionCallback that in theory should work but it is problematic. I think my problem comes from the fact that the callback gets called many times with a different set of selected cells as the input each time. The only case I have attempted to handle is the case where the user clicks on one cell and drags across a group of them. I want only the last one they selected to be left selected. I have not attempted to handle the case where the user holds Ctrl and then starts selecting cells.

If there is a builtin way of enforcing a single selection that would great. I have even tried retrieving the jTable object and setting the selectionMode by jtable.setSelectionMode(0). The place I found that solution says that it works as of 2017a, but I'm using 2017b and it doesn't work. :(