Sunflower stalks will add carbon to your soil. Many areas of North American have lost a lot of carbon from their soil due to too much tillage. So I try not to dig my soil too much, but sometimes I need to so that good stuff goes where I want it. It's a balance.
Walter Byrd wrote:Should I run them over with a lawn mower to mulch? This turns them into powder.
I would worry you would loose a lot to it blowing away. Powdering a little of it to add to potting soil would be different.
Should chop them into small pieces and mix them with the soil? If so, how long? A foot long? An inch long?
I would try a foot give or take. I would dig as narrow a trench as possible, lay the stalk down in it, then cover it back over sort of like if you were planting a potato.
Have you visited our biochar forum? (
https://permies.com/f/190/biochar ) If you can get a lot of sunflower stalks, making biochar, activating it with compost tea + pee, and mixing it into your soil could really help with soil building.