In keeping with weed control – let me remind you of two important facts about cover crops.
Cover crops – a crop sown after the main harvest or in place of a harvest in a garden area – can build organic matter in the soil. We’ve often seen plants such as clover or buckwheat recommended even for home gardeners for this kind of thing.
But if you grow rye, wheat, mustard and sorghum family crops – they actually fight off weeds with an allelopathic effect.
Of all of these – rye is the best. Bar none. It stops weed seed germination dead in its tracks. And the suppression of small weed seeds lasts for up to 2 months with rye.
However, if you till it into the soil the effect is lost as the chemical disperses.
So after you’ve harvest the spinach, sow a row of rye seed and allow it to stay in place for the summer (that area should be much more weed free next season).
Every time you have an open space, fill it with rye seed. Rye will out-compete the weeds, provide erosion control, add organic matter to your soil.
The following spring, till it in and you’ve got good organic matter.