Can I Configure One Elastic Beanstalk Instance Differently From the Others?

You might also try creating a Joblock table in your database to manage locks. You'd insert a record when a job starts and then delete it when the job finishes. If another instance tries to run the job, it can check if that lock exists in the table. This solution tends to work well in preventing simultaneous executions.

One approach you could consider is not only to use an environment variable but also to check a lock or record in the database. This way, the designated primary instance can manage the execution of the SQL query. Having a unique mechanism to enforce that only one instance executes the query will help prevent a database lock scenario. But you might want to explore the automation of this process, using a secondary script that sets this instance as the primary.