In a situation like that, the propane burner is probably your best option. Just make certain that you
fry each and every one
before it goes to seed. (Most weed seeds can survive a forest fire!) You cannot control seeds brought in by the winds and bird
poop, but if you can control the existing weeds before they reseed, it can be a manageable task. Every time you need a break, just tell the boss "I gotta go check the parking lot...I thought I saw some birds setting up camp there!"