I figured out the answer to my question myself today. Turn off Limewire. Crank up BitTorrent. Open the torrent with BitTorrent. When asked where to save the file, use the corresponding directory in limewire's "incomplete" folder. BitTorrent will then verify the contents of the downloaded file, and resume the download where limewire left off. My download speeds have nearly quadrupled as a result.

I hope this helps somebody!
-Chris