Half Dragon, Half Meme
Since badges are per profile, an option section for them could be put in the Updating Profile Description page, whether it displays as a dropdown, scroll view, or the like. In this system, badges would get 'unlocked' once handled out. Locked badges would be blacked-out, unselected unlocked badges would be darkened, and selected badges displaying their normal colors. Unlocked and locked badges would be in groups, separated by a line or something similar so unlocked badges can be easily found. This would allow the user to switch their displayed badges as they please (badge limit allowing) with much less staff work.
Not all badges should count towards the limit, however. Some badges are more then a mere pretty trinket. A few good examples of what I mean are the artist badge and the staff badges. These badges are descriptors rather then achievements. Some possible future badges that this would apply to are badges for being a: writer, poet, game dev, etc. Most (I think it might be a good idea for staff badges to always be on for the sake of transparency) of these badges would still be togglable.
Bare in mind that badges for things such as having drawn 1000 artworks, metadata changing, writing (insert amount here) words and other badges that relate to non-limited badges would still be considered limited badges as they lack the importance of their related badges.
I think this system would improve how badges are handled, allow for automating certain badges and greatly lessen the work on staff.