Daron, have you had the soil tested? Do you know if any of the clay soil amendment tricks will work to open up the soil structure and increase infiltration?
The last time I had to deal with heavy clay soil, it was in a finished housing development where they had scraped away all the topsoil, smoothed the largely clay subsoil out into an impermeable barrier, spread some of the now-dead topsoil back in a layer of about an inch or so, and dropped sod atop it. It was a muddy mess.
After most of the grass died, first because it drowned, then because it baked, I tested the soil, which showed a calcium deficiency, and a lack of organic material.
So I made a bunch of garden beds in one backyard. I got a truckload of ramial wood chips dropped off by a local arbourist I know, took some buckets of gypsum powder and grit that used to be untreated drywall until it fell off a truck, scraped back the topsoil and spread the amendments all out where I wanted them, and forked two-thirds of the wood chips and all of the gypsum into the top foot of the clay, reserving the rest for mulch.
I cannot adequately express the change that took place. The grass, as it turns out, wasn't as dead as I had thought, because along the perimeter of the new beds, it all came back lush and green. The next major rain event showed that, while on the unamended former lawn, ponding still occurred, the improved soil soaked it up, and the area of effect extended to just outside of the greened perimeter areas of the beds.
Not that I am suggesting that you improve your soil to allow a traditional drain field, of course, but I think there are a number of ways to use improved soil around the perimeter of the ponds you're considering to enhance the cleaning effect, and mitigate the risk of travelling pathogens, simply by increasing the vitality of the soil, and it's ability to out-compete pathogens, and eat them.
There's also the idea, whatever the length of the run of the entire system, that by introducing micro-booms, basically biodegradable fabric socks containing wood chips, designed and inoculated like Paul Stamets' mycobooms, it is possible to encourage the water to zig-zag the whole length of the run, increasing surface area, habitat for fungi and bacteria to do their decompositional duty, as well as spots where reed bed populations can be planted, acting as physical filters in the water to grab and slow particulates and solids for processing.
One concern I don't always see addressed is that of untreated water leaching out of the treatment ponds and channels into the surrounding earth. I like the idea of planting up the perimeters of these constructs with water-loving poo-eaters like willow, building up an artificial riparian treatment barrier, just in case there are leaks.
But let us know how it goes, and good luck.