*sigh*
Okay sbillard, here's some new clues. I changed the 'image size' of the images: options > theme options > image size, and now I can crop fine.
I originally had the setting to be 500, and the setting at "width." This is the actual size of the JPG images -- they are all 500px wide and various lengths. Therefore, this gives me the best image on the ZP image page. When I change it from 'width' to 'longest side' it fixes it. I can now crop. Changing it to 'shortest side' does NOT work. I am guessing this is because the size of the image is still the same. This is consistent on any of the images in this album -- including some images that are originally 300px wide and 600px wide that I included for testing. However, again, it's only on portrait images. Horizontal "landscape" images do not suffer this anomaly.
Now here's the fun part. When I this image size set to 500px 'wide', images in other albums that previously worked suddenly do not work -- they do the same thing. What's the width of the original image? 500 pixels. Now going back to the ZP install that previously DID work, I see that the image size is set to the default of 595 pixels on the 'longest side.' When I change that to 500px 'wide' like the other install -- and then I purge the cache and refresh the database, what previously worked does not. If I go back to 595, it's fine.
So as long as I have 'image size' set to something other than the original size of 500px wide, things seem to work. Obviously, I'd like to keep things at the original size since that gives me the best image. I'll likely have to make my thumbs in Photoshop for this to work. But I hope that this information can give you guys clues so that this can be fixed. I don't know if "500" is the culprit, or what. But at least it's consistent now.
Egads.