From the Small and Organic Farm Advisor Blog Johnsongrass in organics: Mow it? Yes, mow it! Mowing works to at least prevent seed spread and regular mowing will weaken rhizomes. Seed establishment has the greatest potential for the establishment and spread of johnsongrass and must be prevented.
Over the past two seasons I have been involved with testing an experimental herbicide for weed control in alfalfa. There was an initial trial implemented at the Intermountain REC in Tulelake California during the 2019 growing season.