I don't know Django and what Django-specific problems/solutions are available, but AFAIK the only scalable (and largely language agnostic (1)) solution is to break these down and deploy incremental versions of the app.

For example, they give an example where widget_description is being added which must be not null. But this should be two migrations: 1) adding the column, 2) making it not null. And because these are now split, they can make incremental changes to the app to accommodate these migrations - the first version working when widget_description is nullable and the second, after the data is fully migrated, when it isn't.

(1) If you're using any `select *`, it's important that your ORM ignores unknown columns (e.g. newly added). I've inherited systems that used libraries that behaved like this, and it's awful.