Old: While the "quick select" doesn't necessarily have the strict search criteria you're looking for, you might try doing the search and then sorting by file size. Those signatures are rarely larger than a few KB, and I'm assuming the files you'd be looking for would drastically dwarf the signatures in comparison.
New: The optimal method for achieving the methods required (retrieve items that have attachments that are not signature and are retrievable by date) is to use the Thunderbird's "Saved Search Folder" functionality.
Going to Edit> Find> Search Messages, and defining multiple sets of criteria, then clicking the button for "Save as Search Folder" will allow a return of those items, searchable as a normal inbox.
Image of my search criteria: http://i.imgur.com/11Hcw2G.png?1?2961