Had to do something very similar and ended up doing linked check-boxes instead. I actually did a single checkbox field for every selection (under some I actually had hidden radio buttons that would show only if that checkbox was selected). once I had all my boxes created, I just linked them (see code attached). I just passed the value of the check box selected to my next process.

Tato

$('input[id^=Field]').on('click', function(){
  var checkboxlist = ['Field23','Field21','Field26'];
  var clicked= $(this).attr('id');
  var clickedshort= clicked.substr(0,clicked.search("-"));
  $(checkboxlist).each(function(){
     if(this==clickedshort){
      resetbox(checkboxlist);
      document.getElementById(clicked).checked = true; 
      };     
  });     
});
function resetbox(mylist){
  $(mylist).each(function(){
  $('input[id^='+this+']').prop("checked", false);
  });
}