Foxtail is an annual like crabgrass--it will die at frost. You don't need chemicals--until next year. LOL!
Wildflower meadows require a lot of hand weeding--unless you can tolerate a lot of weedy non-flower plants and grass. Can you train goats to eat the grass and skip the flowers?
However, since the foxtail is an annual which drops seed in the fall--you should be able to use a granular crabgrass preventer in the spring and prevent most of the foxtail. You will have to use an organ-grinder type of belly-carried fertilizer spreader and walk over the area; the fertilizer would probably be helpful in any case. Not organic--but maybe you could mix organic fertilizer (like Milorganite) with it--that would make it eco-friendly.
Naturally, you cannot seed wildflowers at the same time as using a pre-emergent--you have to wait 8 weeks. Planting perennial or annual plants is OK of course.
I suggest adding a few clumps of perennial garden flowers (sort of domestic--not exactly wildflowers). This would add a bit of extra color. And feel free to add a few (or a few hundred) clumps of domesticated annual flowers in the spring. Sunflower for instance. If you have enough flowers--the grass won't even be noticed--might take a lot. LOL!
You may need to thin out by hand any weedy flowers that are too prolific--like queen Ann's lace for instance. Sweet pea is a good choice for wild flower meadows--but it can be too prolific, spreads too fast at times. Keep an eye out for Canada thistle--spreads fast--may need hand weeding.
Around here we can't burn the residue, so the best time to mow (at 4 inches) is in the spring about tax day--April 15. Try to be mowing before the new plants and new grass have started--so you are mainly getting rid of last years brown residue--plus a few weedy trees and brush.