Maybe Grandmother's Fan like this from
http://www.plainandsimplequilts.com/...%20Tidbits.htm
If you have fewer ties than necessary for an entire quilt, you could make a pillow cover (or covers) in a crazy quilt pattern and embellish ornately with stitching, beading or whatever. I would think that would use more of the tie fabric than just the bottom third and would lend itself to a more public display.