Yeah, I'm not a big chemical fan either, but once you're talking larger areas, it just ends up being your best option. For my weeds in the pastures and natural areas, I use some combo of brush hogging, chemicals, and burning.
When my dad passed away a few years ago, it was right during the main Spring weed season, and the noxious Canadian thistle got away from me in my one alfalfa and grass mix pasture while I was back and forth to CA. I was backpack spraying it with 2,4D and cutting the bigger ones down, but the next year they came back as big as ever (they have a ridiculously large root system). That's when the county weed guys here turned me onto Milestone. Expensive, but it destroys the entire root system. I put it in the backpack sprayer and did miles and miles of walking to spot spray every single one that I saw over a couple of months.
This year I had less than 25% of what there was last year, and much of that is likely just plants that I missed. I spot sprayed all those, and fingers crossed, they'll be pretty wiped out next year.
The key to chemicals is using the right stuff at the right time, which is still a big learning process for me.