By mid-May the most mature winter wheat was ready to terminate, so I crimped it with a 2x4 and some angle iron. That seemed to work reasonably well.
The crimped/smashed wheat then provides a mulch for the warmer weather crop, corn in this case. As the corn matures, I'll plant the next round of cool weather seeds and keep the cycle going. It will be interesting to see how the residue from the wheat is consumed by the soil over the summer. The soil in the garden has been significantly loosened and seems, by visual inspection, to have more worms and organic matter than the prior seasons.