Sorry for the delay in getting back to you.
All of the plants you mention are a lot of work to manage.
Honeylocust sprouts can be managed successfully. The most effective way to treat tree suckers that sprout from root systems is by constantly mowing them down, or using a herbicide. Killing the parent tree of the root system by removing it will cause the root system left behind to eventually run out of stored energy ( in that root system) and sprouts will stop. This can take several seasons depending on how large the remaining root system is.
Here is a response to another question regarding honeylocust sprouts from Univ. of Illinois extension:
" Option #1: Cut all the honeylocust root suckers at the base and apply a small amount of systemic herbicide, such as brush killer strength glyphosate or triclopyr. This only works on freshly cut stumps. In essence, you are introducing herbicide to the entire root system, thereby effectively killing the stump and all future root suckers. This can be done anytime of year, including winter!
Option #2: make a fresh chainsaw cut across the stump, and apply a systemic herbicide. In essence, you are introducing herbicide to the entire root system, thereby effectively killing the stump and all future root suckers. This can be done anytime of year, including winter!
***PLEASE READ THE HERBICIDE LABEL AND FOLLOW ALL MANUFACTURER DIRECTIONS***
Option #3: Contact a certified arborist for on-site assistance." (End of extension quote). To find an arborist in your zipcode search at www.treesaregood.com
Note that you are applying the herbicide just to a freshly cut trunk or sprout, not spraying a large area. The idea is to get the herbicide into the root system, not broadcast it over all the soil. You can use a disposable paint brush to treat the stumps. For seeds that are sprouting, again you mow the young sprouts down before they are too woody.
To control Jerusalem artichoke you pull or mow the young plants as soon as they emerge in spring – preferably when they are about 4 to 8 inches tall. If you have a large patch of Jerusalem artichoke or if the plants are sprouting, you can mow them down. Either method works because new tubers are unable to develop without the above-ground shoots. However, total Jerusalem artichoke control requires you to be vigilant and remove every single sprout. New tubers persist about 2 years, and by constant mowing over 2-3 years you will kill these and gain some control. Glyphosate herbicide brush killer will eventually kill this plant- multiple applications may be necessary.
This fact sheet has pictures and details on the management of this plant:
Controlling bindweed is a lot of work, too. Its seeds are viable for 30-50 years, and its root system extends as far as 20 feet below ground. Again, constant mowing is one non-chemical way to manage it. This statement is from MSU's lawn weed site-
"Mixed results have been seen from various combinations of dicamba, 2,4-DP and other phenoxy herbicides. Control can be tricky since the bindweed is often intermingled with woody landscape plants instead of turf. Quinclorac has been reported to have good activity on bindweed. Try to move as many trailing vines from the bushes to the turf before spraying the turf area. Hopefully, if timed properly, the herbicide will translocate back into the root system of the bindeweed." From www.msuturfweeds.net
Research is being done on controlling bindweed with specific insects, a moth, Tyta luctuosa, and a mite, Aceria malherbae. You may want to note these down and watch for them to become available, if the research shows they work. Or, chech back with us here each season for a status.
Here is a fact sheet, which has several bindweed management techniques:
I' m sorry we don't have better news for you. Unfortunately, these aggressive plants require incredible amounts of labor or chemicals to manage. Please write us again if you have more questions. Best of luck with these weedy plants!