Japanese Honeysuckle is so shallow rooted you can generally pull those out with a riding lawn mower no matter how mature they are. Hook em up and then yank them out. All the others you mentioned, with the exception of the Phragmites australis and the Lythrum salicaria, can be pulled out with a weed wrench non-chemically if you get them young enough (under a 2" caliper). For mature nasties of Rhamnus spp., Albizia julibrissin, and Ailanthus altissima... I'm ok with using a chain saw on them and painting the stump with an appropriate chemical because they sucker repeatedly and even if you tried to get them out mechanically you'd end up with a crater considerably larger than the size of those really old satellite dishes and then those THINGS would still be popping up elsewhere and you'd still be left with a crater sized hole. I won't use RoundUp though and the surfactant I've been using with Rodeo concentrate and AquaMaster concentrate is this one-
https://www.forestry-suppliers.com/product_pages/View_Catalog_Page.asp?mi=1891
Actually, I'm now using Accord concentrate with the above surfactant instead of AquaMaster but Rodeo is still out there.
Phragmites australis can actually be drowned. All you have to do is repeatedly cut it down below the water level. Incredibly, same thing with Typha angustifolia. Granted, that often requires flooding an entire area and water to flood out several acres isn't always easy to come by however you can sometimes work with nature and get out there late winter cutting them down real low and then just pray for heavy spring rains. Lythrum salicaria is a little bit trickier but I have had ***some*** success digging up whole plants particularly when they've gone terrestrial.
Nothing I've read has convinced me that WHEN USED SPARINGLY, AND IN THE DILUTION RATE RECOMMENDED ON THE DANG LABEL, that Round-Up has much environmental impact. It DOES have environmental impact...but it's minimal.
Gosh, ever since I took that adult continuing ed class on how to do Internet searches I feel as if I've slept at a Holiday Inn Express every time I google...
https://www.catoxics.org/pdfs/cottonwoodcrAppendixA.pdf
Selected excerpts from the above-
Product: ROUNDUP (also Rodeo, Accord)
Active ingredient: GLYPHOSATE
Type: HERBICIDE, (Systemic)
Other ingredients: includes polyethoxylated tallowamine (POEA) and isopropylamine
Although the active ingredient for Rodeo and Accord is glyphosate, they are NOT formulated with polyethoxylated tallowamine although RoundUp is.
TOXICOLOGY
Active ingredient
While often touted by manufacturers as relatively safe and nontoxic, glyphosate and its formulations can in fact cause serious health repercussions, most commonly respiratory or contact symptoms. The eye and skin irritation is sometimes quite severe and can persist for months.5 Roundup is a potential endocrine disrupter, depressing cytochrome P450 activity in human placental cells and thereby potentially compromising toxin metabolism.6 While glyphosate is not classified as a carcinogen or mutagen by the EPA, a widely received Swedish study has linked glyphosate exposure to the lymphatic cancer non-Hodgkins lymphoma.7 Additionally, glyphosate is nitrosated “very readilyâ€