Well, I can assure you that the pink and purple thistles were plenty evil
too, and they were perennial clumping machines. I let a few stands go out in my wild field and dug out the rest (constantly). I understand that yellowstar is an annual--you probably have about a 20yr seed bank of it ready to go with every soil disturbance.
I don't know "the answer". Burning is scary, but it's fun too. It might work better than plowing if your goal is reclamation
and it occurs to me that what I think of as bunch grass might just really spread well after plowing? I don't really know--talk to all the experts and your neighbors.
I do know that my current yard was a vacant lot for a long time and that I have a wicked seed bank with an amazing variety of nasty stuff that I don't want to encourage and a few surprise gems once in a while. Any time I disturb the soil I get a flourish of weeds--
You know how some folks aerate their lawns and that's supposed to be a good thing?
Well we tried that once after driving a lot of heavy equipment over the lawn, once we had established a lawn (from seed btw and that wasn't easy), and every single one of those little dirt plugs sprouted a weed riot
and likewise, every time I plant something in the gardens I always get more than I bargained for where I disturb the soil.
So, for me--here, mulch is a great helper, as are groundcovers, and no tilling, aerating, mixing, etc., after the initial set-up seems to work best--especially amazing results with the veggie garden.
Given my experience with this mess, if it were me, I might be inclined to explore cutting and burning as opposed to plowing-up an acre and liberating all those seeds to compete with the seeds I'm sowing...