I had a slightly different problem. Brown slimy roots but not caused by pythium. I have not used food grade h202, but store bought h2o2 is safe enough that I have sprayed it directly on my roots with no problems. It does a good job of foaming the dead stuff away visually improving the roots almost on contact. I always felt that it killed a lot of the stuff on the roots, but it was never long, sometimes only a few hours, before the problem came back if I used h202 alone. I've added it to the res water, as much as 1 bottle per 3 gallons, with no obvious stress to the plants, but it still didn't keep slime from taking over the root zone.
I once soaked the roots in a 10:1 mix of bleach for 24 hours. I have no idea how that ratio compares to the recommended dosages, but it didn't stress my plants. The roots fizzed and the stuff around them died. I rinsed them and put them into a fresh res and all seemed well for a few days, but eventually the slime came back. Same thing with Physan 20; it does a great job of killing whats there but unless you run it all the time, the slime comes back. I once ran Dm zone + h2o2 + Sm90 and still had slime take over, even with low res temps and high dissolved oxygen. So I would not reccomend any of those products for the problem I had, but for run of the mill root rot they work well.
I was just thinking that DM Zone does a great job of keeping away root rot and also killing bugs and worms in the res, while at the same time being very economical and simple to use, without having to wonder if it's safe for the plants. I suppose that sounds as if i am implying that bleach isn't safe, but that isn't my intention.
I had to switch to using beneficial microbes in my res to fight off the slime problem. I am now hoping I never see any sort of worms in there, as Id have to sterilize them and kill off my micro army in the process, giving the slime a chance to come back.