Oh no, I'm so sorry.
I am a fan of bleach, and there will be a cacophany of nay sayers. But bleach is not harsh "chemicals", at least, not after you dilute it down. If you add it to your reservoir, the bubbles will evaporate off the bleach in a couple days.
I would add 2 tablespoons (30ml) to your tank, either now or after you change your fluids, but you can just do it now, and let it go for a day or two. Then I would take your net cup out, and use your dish sprayer to wash off as much brown schmoo as you can. It may be worth it to trim your roots to about 8 inches hanging down, and then it will be easier to wash the roots.
Put them back in a fresh, disinfected tank with 2 tablespoons of bleach and your usual nutrient mix. Don't worry about pH for the next 48hours.
After 48 hours, check your roots again, they should be less brown and stinky with fresh white roots growing out of the brown stuff.
If you really can't abide the idea of bleach, hydrogen peroxide will have a similar effect, but you have to use more of it at a time.
Of course, you must also find and eliminate the cause of your root rot, especially light and heat in your reservoir.