How about an update almost a year later.....this stuff sucks!
Spoke with the extention agent this spring and he said to "dry bed" it. Which I believe was to kill, and keep tilling, repeat. That didn't work...I ended up spraying with 2-4D earlier in the summer, that kept it at bay for a bit. Then another round took off. Bash my head...
It's like getting married. Once you got it, its hard to part with it. Read that any way you want.
Herbicide: Banvel (dicamba) + 2,4D, + MCPA of one sort or another. This mix will kill all broadleaf weeds. Spray the pigweed before it hits 4" tall. Three inches is great if you can get there. Then, I'd plant cereal grains. The herbicide is "friendly" (in an Afghanstan sort of way) to corn and cereal grains like rye, oats, and wheat.
The problem with turning the soil like your agent suggested is your always bringing new seed to the surface. I read somewhere on the Internet (so, it must be true) a (one) pigweed plant can produce thousands of seeds and they will lay buried in the soil for decades!! So, stop tilling!
Another option is glyphosate! Yes! Not all pigweed is resistant. But, Monsanto has hedged their bets and has packaged glyphosate with banvel (dicamba). It's called RoundUp Extend. I'm not sure it's approved yet.
The thing about Banvel is that it has some residual - that is, it stays in the soil and mows down little pigweeds LONGER than 2,4-d. If I remember correctly, 2-4, D's half-life is seven to 10 days depending on soild temps. Banvel 's half life is quite variable, but it leaches out of the soil in 3 - 12 weeks. So, maybe you can get an effective action twice as long from dicamba.
All you can hope for is to keep it under control.
Good luck!