Like a few other users earlier in this thread, I noticed that Image Handler wasn't displaying the larger additional images properly, even after I upgraded to version 3 (maybe this is why the person who set up the site I've been maintaining ended up turning Image Handler off; I only looked at it again after someone else in the organization complained the preview pictures were too large): If the original filename were like images/product_01.jpg (for a product with main image images/product.jpg), it would try to load the larger image from images/large/product_01_LRG.jpg, even though the actual image would have been in bmz_cache, just like the larger version of the main product image and the thumbnails for main and additional images (which did show up correctly).
I got the impression, from reading this thread, that this issue had been fixed in Image Handler 4, so I decided to compare IH3 with IH4 and apply those changes that were not specific to Zen Cart 1.5 (things like better code quality and new defined symbols), and after I uploaded the changed version, the additional image popups finally worked; I plan to similarly backport the IH4 improvements into the default IH3 and submit that as an update (now if I could only set up an IH3 auto-patcher like the one in IH4...that's probably too onerous for me, though).
It's good that this tactic worked, because I had been looking at the code directly and not figuring out why the main product image popup referred to bmz_cache but the additional image popups referred to the old ZC-style path.
For the record, when I took over the store, it had Zen Cart 1.3.8 and Image Handler 2 (which was disabled) and some other mods (including Dual Pricing, which I figured out how to fix about 4 years ago on this very forum) that made it impossible to just copy over the core files from IH3 when I updated it (which was years after updating Zen Cart itself to 1.3.9h, and during this whole time I would just resize images by myself because I like manually optimizing product images to optimize bandwidth).