Blocking a dialog content (with the radio boxes):
It seems the problem comes from the modal: true option of the #ajax-dialog dialog. If you set the option to false, it works as expected. Upgrading to the latest version of jquery and jquery ui did not seem to resolve the problem.
Note the option baseZ in this case, this is the z-index of the overlay, which has a default value of 1000. Set it to something higher than the dialog to cover it.
You can use the plugin BlockUI which allows blocking the full page or an specific element. it works by showing a overlay div (over the page or the element) forbidding any interaction with the underlying content. You can display a message and customize the look&feel.