I use a hot mix of roundup on trees that are shorter than I am with great success. They are usually 1 inch or less in diamater.
Remedy and diesel can be used at anytime of year, but use the tordon when the sap is flowing down instead of up cause that may push the tordon out.
There are two types of conductive tissues in plants and trees, xylem and phloem. Xylem brings water and soil nutrients up from the roots, phloem moves the products of photosynthesis down to the roots. This occurs whenever the plant is actively growing. As long as you get the Tordon to the phloem, it should make it to the roots to kill the tree.
If the locust is honey locust, I would advise leaving some of these trees - deer really like the pods & I have witnessed deer walking through corn to a honey locust tree to eat the pods. Honey locust trees are quick to colonize an area, which can result in a monoculture, in which case you should remove all but a few. If you only have an occasional honey locust, I would leave them & know that deer like to eat the pods.
Mick