You will likely have to resort to using a systemic herbicide to kill the Houttuynia roots. Even though it can work well, repeat treatments will likely be necessary for established patches of this aggressive weed. Follow all label directions for the most low-risk, effective application of the chemical chosen. A product using the active ingredient glyphosate (the one common to Roundup) is probably your best bet, but we do not have local research as to which herbicide approach is the most effective.

Some herbicide products may allow for (or even encourage) the addition of a surfactant upon mixing a solution for application. Surfactants, also called spreader-stickers or adjuvants, are additives that help a herbicide adhere to the leaves (in this case) or work more effectively in other ways. Here, it would help a spray stick to the leaf long enough to be more fully absorbed instead of dripping off. These products are sold alongside pesticides in garden centers since the two are often combined for certain uses, though not every product benefits from their use, so always verify this with the label usage details.

Early autumn may be the most efficient time of year to attempt herbicide treatments, since the plant's deciduous leaves will be transporting more carbohydrates in the sap down into the roots for winter storage, and the absorbed chemical will then be able to "hitch a ride" more easily into the root system to cause dieback. Regardless of the time of year, plants successfully treated might not show obvious signs of dieback for days or even a week or more after application, so don't pull or dig them up until you're fairly certain they're dead.

If you wish to avoid herbicides, your only recourse will be to physically remove what you can by digging-out roots and to constantly keep trimmed-down all above-ground growth so the plant cannot photosynthesize. We realize you said this is not likely feasible for you, but we mention it just in case you wanted to try (or try it on a portion of the patch). Every time a weed can regrow for a while, the plant is recharging the root “batteries,” so to speak, for continued regrowth. That battery is depleted a bit every time the plant is forced to replace foliage, so if you can keep "discharging" that battery by making it keep regrowing without being able to photosynthesize, eventually it will starve and stop returning. This method might take years to achieve full eradication for well-established weeds, and will only work well if you have full access to the continuous patch. (For example, if part of the plant's spread continues into a neighbor's yard that isn't able to be controlled because you can't access it or they aren't willing to help combat it, that foliage could still fuel regrowth back onto your side unless you install some sort of barrier along the property line.)

Denying the foliage light instead by smothering the patch with a light-blocking tarp probably won't work as well in this case as it might for other weeds, because this species could just keep creeping outside of the covered area to resume growing. Plus, any desirable plants growing among its leaves would be killed as well by the tarp. (Granted, desirable plants would also be damaged or killed by herbicide if directly exposed.) You can of course try it and see how it goes, or use this in combination with other approaches (smothering, then spraying what foliage reappears after the tarp is removed).

We are not aware of Houttuynia spreading via seed, at least not into natural areas (fortunately). Spread seems to be primarily or entirely vegetative (that is, from runners or pieces that break off and root elsewhere).

Miri