A WordPress plugin that installs a widget holder under Appearance > Widgets and a plugin in the content editor. Any widget from that holder can be inserted inline into page content. The MCE plugin inserts the shortcode that triggers the plugin to render the specified widget.
I've made this for my own purposes really and I haven't made it a publicly available WordPress plugin. I haven't spent the time to see if it's up to that yet and I don't want to have to support it. Other developers though are welcome to it.
All code is adapted from the WP Codex and user comments.