Thanks for your input Katie. Good to hear that you have some evidence that headway may be made with physical removal.
Christina Baugher reached out to her contacts and came back with this information...
Susie Iott reached out to Erin Hill, a weed diagnostician at MSU. Here is her response about the chameleon plant – I hope it helps!
“Here’s a small write up I put together as the control options should be similar to those for other aggressive groundcovers like goutweed. Note I do not have direct experience with this plant, but this should be effective. It’s tough to find info even within Google Scholar as apparently it has a lot of touted medicinal properties…who knew.
Chameleon plant (Houttuynia cordata) is a perennial plant in the lizard tail family (Saururaceae). It is not native to Michigan and often used as an ornamental and for groundcover. This plant has the ability to form large colonies from underground rhizomes but it can also reproduce by seed.
Control of chameleon plant can be very difficult, depending on its location. Digging up the root system and removing foliage are certainly options for control and will weaken the root system over time, but it could take a very long time. The use of landscape fabric plus mulch to deprive the plant of sunlight may work in certain situations on a small scale, however any holes in the fabric for desired plant may offer an avenue for emergence. There are no selective herbicides that will kill this plant and not affect desirable broadleaf plants. Depending on how interspersed it is, how big the area is, and how large of a nuisance it is, it may be possible to spot treating with a herbicide such as glyphosate (Roundup® Weed and Grass Killer, amongst others). Products containing glyphosate will injure other plants contacted during application (i.e. green tissue, damaged/green bark, exposed roots). Multiple applications may be necessary for complete control. Glyphosate does not have activity in the soil, so once you are satisfied with your level of control it is safe to replant desired species. Remember, always read and follow labeled directions.
*If it’s even in an all grass situation there are likely some selective herbicide options.”