I already think I may have found a solution with the "Selection2Clear" plugin.
I tried what you had suggested but I did a Shift-Magic Wand on all of the transpartent parts of the image at one time (had to adjust the Tolerance to get the multi-selection correct), then did a Shift-Paint Bucket to fill all of the background to black and then saved the image.
Then, while the image still had the transparent (now black) parts of the image still selected, I finally used the "Selection2Clear" plugin and the resulting image once saved no longer shows up with a halo effect on the edge where the transparency begins.
Thanks again.