If the plot has never been a field or not recent, I think you are best killing it twice. Round-up the whole field, wait 2 weeks and kill it again. You will be surprised what weeds can make it through if the weeds were real thick. It also depends on how well it was cut to the ground before killing it. I had a similar experience and re-planted the plot. You may have some results by mowing it a couple times a year.

Also, you can spray weed and grass killer on the plot that won't hurt your plants (check label). Good luck.