Aquatic polyculture: what else can I plant in my water chestnut buckets and tubs?

So, I'm starting water chestnuts again and getting my buckets and tubs organized and filled with soil. Last year I was impressed by the extent to which my water chestnut containers did not breed mosquitoes; I believe it's because of all my volunteer frog squads who moved into the tubs, as well as perhaps having something to do with the dragonflies that were breeding on my chestnut stems.

Even so, my water chestnuts last year were a monoculture. Soil, water, water chestnut plants, and volunteer wildlife. Plus quite a bit of algae.

This year I'd like to mix it up a bit, and have an aquatic plant polyculture. I don't want anything with a too-extensive root structure, because harvesting the corms is already hard enough-- the water chestnuts themselves seem to need all the available root space in my containers. So I'm looking for temperate-climate (or subtropical at most, nothing tropical) aquatic plants with modest root systems (maybe even floating plants?) that have some utility: more habitat for the frogs and bugs, pretty flowers, or even good for scooping out by the double handful to use for mulch in my container garden.

And because I don't really have access to an aquatic plants nursery, I need something that I can grow from seeds or from starting material I can get cheap on eBay or wherever. This is for fun, there's really not much budget.

I welcome brainstorming and speculation, but if you've actually got experience growing other stuff in with your water chestnuts that's what I really want to hear about!

One interesting plant that I'm finding references to is azolla -- an aquatic "weed" that has fixes nitrogen and has been used to increase rice production in paddies for at least 1500 years.

+1 on Azolla. Grew it in tubs with various water plants, including water chestnut and it seems to increase the growth rate of other plants in the system ( I never measured this or ran a controlled experiment, but that was the impression I got). It doubles its biomass every couple of days ( at least under Hawaiian conditions) so must be continually harvested from the waters surface or it will form a mat that smothers everything else, but the upside is that it make first rate mulch or compost.

I finally found some atoll a last year. introduced some to my pond- where it utterly failed. Not a clue why.