Thanks! Really, credit goes to the plugin (which piggy backs on the Fourier plugin) and a guide I found for tweaking it.
Plugin: http://registry.gimp.org/node/24411
Guide: http://www.zoyinc.com/?p=1529
I had to do undo part b of the tweaks because it caused an error, but otherwise it did good. I ended up using 50 for sensitivity and 7 for “ratio for middle preservation”. No despeckle.