If business class if fully booked, you can not buy a J class ticket. Period.

You might be able to buy on a different flight, clear the upgrade and then request a change to your desired flight. I'm pretty sure your original ticket must be one that allows a date/time change. I don't know if making the change would require both ON and J space or just ON space to be available on the desired flight in order to make the change.

Since you can cancel within 24 hours, why don't you give it a try and report back the results.