It is not a riparium planter, but I have spearmint growing in a marina air driven HOB breeder box full of hydroton capped with "natural" aquarium gravel, outdoors. I heard that most mints go crazy in hydroponic systems, so I figured this would keep oxygenated air passing over the roots, like a hydro setup. The spearmint is going nuts but unfortunately so is the green water.
I bet if you just laid a bundle through a mesh or chicken wire lid and hanging into your tank water it'd root in no time and spread everywhere.
I've got spearmint in an indoor riparium planter but there's not much light up above my tank right now (2 2-bulb shop lamps across the top and some track lights vaguely aimed at it from far above). It's rooted, but is only stable and hasn't thrived like the creeping jenny next to it which has spread both above and below the light canopy to take advantage of the more intense light there. I think with more light the spearmint will explode even without additional oxygenation of the root cluster.
Spearmint is the only edible I've tried in a straight riparium environment, but I hear that lettuce grows great hydroponically too. I don't quite see how you could grow that just through a mesh lid though. Might be time for some net pots (support the least skeevy of your local hydroponics stores) and a hole saw/acrylic sheet, which would be an easy enough project, and let you cut off lettuce as you need it, which has never been in contact with the aquarium water, and pull the whole lettuce heads out with a root ball and replace them with a smaller start when they start getting too gangly or whatever. And if lettuce roots start rotting in the aquarium water, an air stone under the root ball to cycle water through or even a powerhead to just circulate water around the tank will probably fix it.