I live on six acres with half being mature hardwoods. For the past 10 years my wife and I have maintained a vegetable garden of about 7,500sf (50'x150'). For most of that time we have struggled with both pigweed and thorny pigweed, mostly from my inexperience 10 years ago when I applied several tons of cow manure to my garden. So for the next several years we have decided to fallow the garden in an effort to smother out the weeds. From what I have read 5 years should all but eliminate pigweed.
I have been cultivating mason bees for a few years now. There were hundreds of them using one of my sheds when I moved in and we have gotten along ever since. Lately I have been building nesting trays and boxes to support a few thousand residents and have decided to expand to other types of solitary bees, notably leaf cutter bees.
I am considering moving to European honey bees soon, but for now there are tons of them around from other local hives. And they love my property as I garden organically and let the native flowers grow in areas I'm not using.
So now to my question. What should I plant as a cover crop to help my bees, but also to smother pigweed? I don't mind rotating crops or mowing a few times a year, but let me tell you pigweed is very tenacious. Obviously a small amount of research will give me a list of cover crops beneficial to solitary bees, but I have yet to see a plan that might help me smother the weeds.