I don't think it is that difficult or expensive to control knotweed using modern methods, at least on a small scale. I started investigating this in order to control a persistent patch of knotweed at my parents' home, but unfortunately, the patch was cut down before I could implement what I think is the most safe and sustainable method, at least for isolated patches: stem-injection or hack-and-squirt with the herbicide imazapyr.

Imazapyr is slower-acting but more effective than other herbicides. As you can see in this study, which compared several herbicides applied with spraying, the imazapyr formulation performed worse than all others for up to 58 days, but after 333 days, the knotweed was 95% gone, better than any others, even the formulation that mixed imazapyr with glyphosate.

Evaluation of Imazapyr, Glyphosate, and Triclopyr for Japanese Knotweed Control
https://weedscience.ca.uky.edu/files/japaneseknotweed2005.pd...

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Here’s another study - 96% of imazapyr-treated trees were in the highest defoliation class vs. 62% for glyphosate:

Efficacy of ‘hack and squirt’ application of imazapyr, triclopyr, and glyphosate to control the invasive tree species Chinese tallowtree | US Forest Service Research and Development

https://www.fs.usda.gov/research/treesearch/35461

"These results indicate that imazapyr can be used to eradicate Chinese tallowtree by ‘hack and squirt’ injection without short-term (12 months) damage to dominant live oak trees."

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Controlling Knotweed in the Pacific Northwest (this mentions stem injection using glyphosate)

https://www.invasive.org/gist/moredocs/polspp01.pdf

"Although time-consuming, not only does this approach essentially eliminate drift, but Clark County (WA) Weed Management reports obtaining 100% control in one treatment by injecting 5 ml of 100% Aquamaster or Round Up Pro into each stem of a given clump. More than 20 patches were so treated"

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Here they also use glyphosate:
https://web.archive.org/web/20030404152410/http://www.co.cla...

"If 38 of 50 canes are injected, expect the twelve that were NOT injected to survive and reproduce. EACH CANE HAS ITS OWN SEPARATE RHIZOME SYSTEM. Even though the injection process is initially time consuming, it is more cost-effective than several trips to the same site for foliar applications made over years with minimum results."

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None of these studies mention the specific technique of using stem injection with imazapyr, which I think is likely to be the most effective method. Although I haven't yet tried imazapyr on knotweed myself, I used an extremely minimal amount to kill several different species of obnoxious shrubs.

I used it to kill:

- Japanese barberry

- Sumac

- Elm saplings

- Fox grape

All these had been growing from the base of the external walls of my parents' house and had been uncontrolled for decades despite (probably-not-frequent-enough) cutting.

The amount I used was maybe a fluid oz. in total for all of these, and that was probably overkill. I just cut a flap into the bark in such a way as to maximally expose the cambium, then applied a few drops and tied the flap closed with some string. I did this to some sumac suckers right in the middle of a bunch of my mother’s day lilies and my stepfather’s blueberries and they weren’t affected at all.

In the case of the sumac and others, it took a couple weeks before the plant was visibly wilting, but after a while, even untreated suckers several yards away died. The fox grape didn’t show signs of wilting at first, but was dead by the following spring (I treated in early July, which is actually less than optimal. Late summer is recommended because of the predominant direction of sap flow at that time - from the leaves to the roots)

I have a meat syringe which I plan to use to inject knotweed when the opportunity arises.