There can be more than one path here, and it depends on a couple of factors:
Do you want all the images to be competitive in image search, or are you okay with only your main product image being competitive?
Are those zoomed-in images crucial for individuals with accessibility challenges, or is it okay if screen readers and other such technologies skip over them altogether?
One path you can take is to give your main product image strong alt text, and the rest of your related images minimal alt text with slight variations:
Main image - "Widget by Company, the thing that does some things."
Zoomed-in image #1 - "Widget, view from the front."
Zoomed-in image #2 - "Widget, another view."
Another path is to give your main image a great alt tag, and let the others have duplicate alt tags. The reason this is not recommended, as you mentioned, is that it may not be great user experience for screen readers, and might devalue those secondary images for search, but technically you won't be penalized, so it's okay to do this if it fits your particular case.
If those supplemental images are not crucial at all, you can leave your alt tags blank, as if those images were design elements. (Web designers leave images like lines, geometric shapes, and background gradients without alt text, which makes them virtually invisible to screen readers and mostly ignored by search engines.)
Here's a related discussion on Moz's boards.