i am aware this topic is over a year old, how did you end up dealing with mimosa pudica unns boy?
on my land, here in vietnam, i have lots of that weed as well. first i was going to rip it out a lot so i can walk barefeet everywhere but then i saw the rich nodules on its
roots and something clicked in my head - this is how my internet research on
permaculture and a much better garden started ^^;;
anyhow, i am not so far into a perfect garden/ food forest yet but - as a legume mimosa pudica is excellent
compost and mulch material and i am using it as living mulch under some
trees and even flowerbeds etc, aside from helping the soil i think it keeps the dogs from rummaging in those places because it is so prickly. its flowers are great pollinator instect attractors too!
to get rid of it i think ripping out is your best option. ripping it out (and compost it) before it can throw seeds, its how i killed almost all my tropical kudzu (Pueraria phaseoloides ), which i now let come back once i realized how useful it is. i noticed the end of the rainy season is a good time to remove plants before they seed since things flower and seed when the dry period starts in this tropical region anyway.
my husband had this land cleaned up a couple of times to the point of bad soil erosion and then a cogon grass invasion - which i am battling now by ripping out in some places and letting mimosa pudica and tropical kudzu grow over it in others.