Add-Migration without parameterless DbContext and DbContextFactory constructor

My application has no parameterless constructor at my DbContext implementation and I don't like to provide a parameterless constructor to a IDbContextFactory<> implementation.

The reason is I want to keep control where the DbContext points to. That's why all my constructors will ask for the ConnectionStringProvider.

public class MyDbContext : DbContext
{
    internal MyDbContext(IConnectionStringProvider provider) : base(provider.ConnectionString) {}
}

and

public class MyContextFactory : IDbContextFactory<MyDbContext>
{
    private readonly IConnectionStringProvider _provider;
    public MyContextFactory(IConnectionStringProvider provider)
    {
        _provider = provider;
    }
    public MyDbContext Create()
    {
        return new MyDbContext(_provider.ConnectionString);
    }
}

I definitely don’t want to add a default constructor! I already did that and it crashed on production because of the wrong connection strings inside the wrong App.config or assuming a default connection string like the default constructor of DbContext does. I would like use the same infrastructure on

• Debug/Relase (and only inject a different IConnectionStringProvider)
• Calling Add-Migration script
• Running DbMigrator.GetPendingMigrations()

Currently I get some of those messages:

The context factory type 'Test.MyContextFactory' does not have a public parameterless constructor. Either add a public parameterless constructor, create an IDbContextFactory implementation in the context assembly, or register a context factory using DbConfiguration.

---UPDATE---

This might be a duplicate of How do I inject a connection string into an instance of IDbContextFactory<T>? but it has no solution. I explain why:

• I always use Add-Migration with connection string, so how can I provide a DbContext or IDbContextFactory<> that consumes it? Instead of parameterless constructors?

  Add-Migration MyMigration -ConnectionStringName "MyConnectionString"

• The same problem here: I use DbMigrator.GetPendingMigrations() which also asks for parameterless DbContext or IDbContextFactory<> implementations.

As far as I understand EntityFramework violates encapsulation by implying default constructors and causes temporal coupling which is not fail-safe. So please propose a solution without parameterless constructors.