Hi Kip,
Ok that's what I thought you wanted to do, but needed to make sure. You can't really do this using one 'set' of radio buttons or group of check boxes for the reasons you mention, plus the fact that you can't predict which of the available option will be applicable.
So you need to do this with 2 sets of options. The first set you'd make a requred radio button group, the second a group of optinal checkboxes. Though of course this would be a strange layout.
i think what i would do is split it into a Dropdown and a group of checkboxes. So in the layout all you need to add is room for a dropdown box.
In the dropdown box add all the possible options and set it to required`.
Then leave what you have already as optional checkboxes.
You can also take it a few steps further.
first add an extra option to the checkbox group something along the lines of 'no additional reasons'.
so now you can also make this group of checkboxes required and prevent people from skipping it.
you could also add conditions to the checkboxes.
for starters you could hide all checkboxes and only show them when a selection has been made in the dropdown
also you can keep on hiding the checkbox for the option selected in the dropdown, so you don't get an option doubly selected.