Vinegar / water solution in a pump sprayer will work. Used it to kill off my old lawn before reseeding last spring.
Cut thistle to ground level.Pour hot white vinegar or hot apple cider vinegar then pour on alot of table salt on cut parts. (do not dilute vinegar)
Catch them when they are relatively small and they won't have such a substantial main root. Water it well and you should be able to easily pull it up. Make sure any flowers or buds on existing thistles are removed before they can go to seed to prevent new ones. I am never rid of them as I have a neighbor that does nothing to the weeds in her yard and they blow into my yard. I found that pulling them young was the easiest way. I also use Roundup when I find one that has gotten too big. The cancer it causes is in people who work with it on a daily basis for years doing yard and garden care as a living and not taking precautions, it will not cause cancer with occasional use and taking precautions such as gloves. In the yard I use the one that is safe for grass and you have a choice between spray and foam. The foam is the best, there is no overspray and you can more easily target what you want to kill. For larger weeds like that thistle that was missed and got tall in the hidden spots, I cut it off about an inch above the ground and put the roundup on that and they never come back, it gets to the big tap root easier and quicker. I hope this helps you Teresa! Have a great Holiday Season!
Adding food coloring to Round Up in sprayer so you know where it is being sprayed also gives you more control over safety.Keep spray nozzle close to plant, don't do it in wind,don't walk in wet spray,use gloves. I'm one of the people who used Round-Up for over 20 yrs as landscaper/gardener even before it became available in residential market ,that was 25 yrs ago(I've gotten sicker from some of the scripts my Dr. has tried to get me to take). As you stated it is from mis use/neglecting safety measures, any chemical on market that has precautionary measures on labels and says hazardous to anything is dangerous even the stuff most of us use on our pets everyday,paints, household chemicals.
First off, I would not use Roundup. This is why. https://www.sierraclub.org/sierra/new-study-shows-roundup-kills-bees
Then, Just get out your kettle and boil some water. Boiling water kills most weeds. I hope this helps.
I dig them up.