When I click the link all I get is a 1 inch x 1 inch blank box

testing with a single group

config.doksoft_special_symbols = '0x1F00-0x1FFF';
config.doksoft_special_symbols_images_allowed = true;
config.doksoft_special_symbols_images_by_default = false;
config.doksoft_special_symbols_images_font_default = 'Arial';
config.doksoft_special_symbols_images_font_size_default = 12;

Hello, I have tested your case and on my PC I see no problems with displaying popup panel.

But this probably does not matter. When you have seen your problem we were already in progress of upgrading this plugin. Currently we published it on files.doksoft.com and you can update.
The plugin became very similar with CKEditor Font Awesome plugin. Currently it can not be opened as popup (only as a dialog) but got a list of new features.

Please try it, I hope you will like it.