Deb, one non-chemical method that has been used around here is to just spread clear plastic (painters drop sheets work fine) over the weed-infested areas when it's sunny. One good hot day will often kill off the tops very effectively.
Now, with a deep-rooted perennial weed like this hawkweed sounds like, you may have to continue to do this several times through the season to eradicate large established plants. Might not be practical to consider, on a 40 acre scale, I guess. But it might be easier and just as effective as weed-whacking.
Nice area of the country up there in the Okonagan - I was born in Trail BC and spent my summers at Christina Lake until my teens, so pretty familiar with the hot, dry summers up there!
