I do not think any of the listed plugins should conflict with Content Aware Sidebars. I have tested most of them.
The JS functionality in version 1.3.5 relies on:
jQuery
jQuery UI Accordion
jQuery UI Autocomplete
These can be found in WordPress Core as of version 3.3+.
If the list disappears, it sounds like a conflict. To figure out if it is and what the conflict might be, go to the sidebar editor and open a JavaScript console in your browser (for Chrome and Firefox: CTRL SHIFT J, for Internet Explorer 11: F12) and refresh the page. If there are any JS errors, they will be shown in the console.
By default in version 1.3.5, only the 20 latest items of the specific content (posts, pages, authors etc) are listed in the sidebar editor. The rest should be found with the search functionality. By latest, I refer to the creation date of the items.
You can change this value to any other number in the code, of course, but there is no way to reset it from the administration panel.