Set all radio buttons at once – use regular buttons or radio buttons?

On this form, the acceptance criteria is to have a convenience all select for a choice. For example, the user selects no and all the radio buttons would select to no.

However, if a user selects different radio buttons then I need to reflect that in the top left global select radio buttons. Since a radio button group should not be deselected and not left empty. So, I have added a multiple radio button.

My question is, is a multiple radio button a good solution? Or should I change the convenience global selectors to buttons instead of radio buttons?