Try a different approach here instead of enabling Always one selected in multi box itself.
apart from two multi boxes create list boxes for your individual columns and enable always one selected property.
Hide the extra list boxes created.It should work.
Have a look at attached QVW.
Always one selected.qvw 150.8 K
With Always One Selected on the Year field, you will not be able to select 'Variable' in your above example because that implies a null Year (which means nothing selected). So what you are attempting does not work.
Can you not use some other technique to make your user select a year, such as conditional calculation or conditional visibility of the charts?