Hi, Well thistles are a very difficult problem that I've dealt with myself many times on my Iowa farm. Really the only way I've found to work is with chemical sprays. Mowing frequently does help a lot and not letting the plant set seed is essential, but ultimately a spray is the only thing that can really knock back something as strong as a thistle. Now, there's no reason you can't spray and not have it run into your garden. In fact, if you follow label and spraying directions on most any chemical herbicide you should not have any run-off or drift. I don't see why your veggie garden would have problems as long as you spray on a calm day and only spray the thistles without overdoing it.