Sorry, but the WordPress Shortcode API does not support shortcodes with in shortcodes like that. It is not a Connections limitation or bug. There is no way that I know of to accomplish what you wish to do.
If you want … I do have a beta version of the next version of Tile Plus I could send you. The main difference is that it is in the process of being updated to support the Template Customizer, with that you can set a global default for its options. It has been a couple months since I last worked on it so I can not exactly remember what needs complete and what bugs still need ironed out, but it could be worth a try. Assuming this would be helpful if you are trying to set a single default by using that content shortcode.