Whether you use EF or not, maintaining the code's ability to work with 2 consecutive versions of the database is a good (and perhaps the only viable) approach here.
Here are some ways we handle specific types of migrations:
When adding a column, we can typically just add the column (with a default constraint if non-nullable) and not worry about the code. EF will never issue a "SELECT *", so it will be able to continue to function properly while ignoring the new column. Similarly, adding a table is easy.
When removing a column or table, simply keep that column around 1 version longer than you would have otherwise.
For more complex migrations (e. g. completely changing the structure for a table or segment of the data model), deploy the new model alongside backwards-compatibility views (or tables with triggers to keep them in-sync), which will live as long as does the code that references them. As you say, this can a lot of work depending on the complexity of the migration, but it sounds like you are already well-positioned to do this because your EF entities point to views anyway. On the other hand, the benefit of this work is that you have more time to do the code migration. If you have a large codebase, this could be really beneficial in allowing you to migrate the data model to fit the needs of new features while still supporting old features without major code changes.
As a side-note, the difficulty of data migration often makes us push developing a finalized data model as far back as possible in the development schedule. With EF, you can write and test a lot of code before the data model is finalized (we use code-first to generate a sample SQLExpress database in a unit tests, even though our production database is not maintained by code-first). That way, we make fewer incremental changes to the production data model once a new feature is released.