I grew Pennyroyal (Mentha pulegium) in a paludarium for a while. It's one of the smaller mints and I have it growing in a wet area on my farm so figured it would be good. It grew fine but like all mints in was a bit too vigorous. Many herbs, Sage, Thyme, Rosemary need really well drained conditions to survive though. And many get quite large too. Maybe some more exotic herbs might work though.
Did not know there was so much information about aquaponics!
Maybe for my next project!
But I'm sticking to the riparium for the look in my living room for now with this 10 gallon. Just thinking I might get some herbs in there for a bonus but I'm not sure any herbs would grow with their roots in water. Still searching