Looking again at your page that is not loading, there really is nothing being loaded in the browser except for an empty document, no attempt to load either the old jsapi loader or the new gstatic loader. So I would push back on the server guys to look further. If they don't have any error log, whatever log they do have might help. The problem is a complete failure to do much of anything, so if the only thing you are changing is the number of charts, then I would suspect the plugin is the cause.
I doubt it will help, but revisiting the page that loads, I do see that you (via the visualizer plugin) are loading both old jsapi loader and the new loader with:
This is not a good idea, even if it works. The jsapi loader will always redirect the new loader now, so there is no benefit in loading it, and it might cause confusion in the loader. So you should point that out to the plugin guys to get them to fix it.
Good luck.