Converting field of fox tails to safe play space

I just moved in to a farm rental and there is a large fenced pasture for my dogs to play in. However it is totally overgrown with fox tails (tall plants with sharp seed pods that can become embedded in pets' skin). What is the fastest way to convert this to a safe area for them to run in? The ideas I have so far are:
1. Mow frequently (I ordered a reel mower as I hate gas-powered mowers, but I'm not sure how well it will do with the fox tails).
2. Spread lots of seeds for more favorable plants (grasses? wildflowers?).
3. Mulch the entire pasture - this is not really an option due to the size of the pasture.

Any other suggestions?

Foxtail is an annual grass, it thrives in sparsely covered areas.

So to eradicate it the easy method is to mow it short well before it forms a seed head. Next broadcast the grasses, etc. that you would like growing there thickly or in multiple seeding sessions (this actually will work better than one thick spreading of seeds).

If you need to be faster, find some 5-10 percent vinegar (acetic acid) and spray both the foxtail plant and the soil at the base of the plant. This will kill it then you can pull the roots or mow very low and reseed with your desired grasses, etc..

Redhawk

Ugh. Fox tails! 1: you can cut your dogs hair to reduce them from getting Tangled and lodged. However, I knew a beagle that got one stuck in her nose. Mowing makes them shorter. Usually they finish their lifecycles when things dry out. They are soft in early stages. Once they harden, even mowing won't make them less sharp (unless it's mulched real small). Controlled burn could work this year with a heavy replant of other things next year, if your area is safe for controlled burns. Some critters will eat it. Mulch is awesome. Even cardboard or carpet could snuff it out until you can outplant it. Wheat will out do lawn here, so that might work... But it's also kinda pokey, but then, you can harvest it! Sometimes with grasses you can time it so they get cut real short and they don't regrow. Usually at just before ripening stage. There's also something I saw with a tall field of rye and driving over it with a car to crimp it. Funny, but worked. Gotta watch that on dry grass though because it could burn.

Thanks for the tips! Controlled burn is not an option because it would quickly become and uncontrolled burn - too much dry plant matter around.

Any suggestions for quick-growing grasses I could seed? They don't need to be "pretty," just walkable and safe.

Try any of the Fescue varieties, they grow very quickly.

For about as inexpensive a blend as you can buy, look for any that carry "playground" in the name.
Bear in mind though that these may contain Bermuda (quack grass) so do read the list of grasses on the back of the package prior to purchase.

Kentucky Blue is also a good species to grow for fast covering.

Thanks, Bryant!