It seems as though this problem may be able to be remedied by implementing three variables to intercept the data, and then changing the HTML as followed:
<input type="checkbox" name="<ml.varname>_01" value="1">
<input type="checkbox" name="<ml.varname>_02" value="2">
<input type="checkbox" name="<ml.varname>_03" value="3">

Does this make sense?