No help, but this has happened to me also, when judging Florianne after Wicked... quest. I was lucky (I save every time before judging) but it does render the throne/further judging inaccessible. I tried a variety of things - changing the throne type, leaving the room, leaving Skyhold, etc. to no avail, and ended up having to reload.
It happened to me on another playthrough judging Ser Ruth, multiple times I had to reload that one. So it's not clearly a bug with any one judgment quest.
The only thing I found fun about it was seeing Josephine in the advising spot near the throne, then running into her office and seeing her hard at work there. Now you know how she gets so much work in.