I now have all the suggestions made above installed on my MorphOS machine.
The results...
Show Girls steals the show by a long shot!
Not only does it support nearly every format under the sun, it also seems to have the best quality preservation when reducing the size of images.
At first the image becomes blurry as one would expect, but once I run the Sharpen feature on the shrunk image, it almost looks as good as the original.
The only faults I see with Show Girls at the moment is the fact that it does not allow for Palette loading and saving, plus it is not always clear what format I am saving in.
When I hit Save, I can choose the format, and I suppose I just change the extension when saving, but when I choose Save As, I don't get to select the format. Also it does not seem to support saving in BMP, which forces me to return to my Windows machine to change the format so that I can apply the Palette I need for DOOM, and save it again.
Is the author of Show Girls still working on this?