Learn to use a scythe and use it to keep the place mowed.
http://youtu.be/gL2_chKPWjE
Sorry if this appears a bit impractical for you but it's what I would do in your position. I have a much smaller space and still I'm planning to do a course on using a scythe.
Initially there would have to be some investment of time and money but it looks like fantastic exercise, and so elegant!
If you are still thinking about sowing wildflowers, I would forget about applying weedkiller because they would be very sensitive to this.