What I propose you to do – you can create separate galleries for each required category and create general gallery to represent your galleries. So each image in general gallery will have a link to view gallery for some specific category. It can be done like redirect to new page with required gallery.
Also, you can use option “Display only first image” option in galleries for each category.
This way you should place all galleries to one page and each gallery can be viewed in popup by clicking on thumbnail image.