This suggestion isn't edible or tropical, but I guess other people will look at this
thread looking for answers since you made such a nice title.
We've had willows growing on our soapy greywater for 20 years and they are doing great. Our greywater is very low-tech. We just run the waste water through a pipe and then into narrow little irrigation channels that run past the
trees. There are several parallel channels, so we change it every day or three. Interestingly, there doesn't appear to be any buildup of soap on the surface.
Art Ludwig's fabulous book and website on greywater point out that topsoil is aerated and thus is the very best for breaking all that gunk down, much better than buried systems.
Create an Oasis with Greywater, by
Art Ludwig is a great source of information.