EF Core - Set Discriminator based on Joined Table

Question

I have the following mappings in the database:

public abstract class ProductBase 
{
    public string ID { get; set; }
    public string Type { get; set; }
    // Base Properties go here 
}

public abstract class PermissionBase 
{
    public string ProductID { get; set; }
}

public class Product : ProductBase { }
public class Addon : ProductBase { }

public class ProductPermission : PermissionBase 
{
    [ForeignKey("ProductID")]
    public virtual Product { get; set; }
}
public class AddonPermission : PermissionBase 
{
    [ForeignKey("ProductID")]
    public virtual Addon { get; set; }
}

In the EF Core Configuration I've set up the following configuration for Product:

builder.Entity<ProductBase>()
    .HasDiscriminator<string>("Type")
    .HasValue<Product>("Product")
    .HasValue<Addon>("Addon")

I need to use the Discriminator value of Product in the Permission table hierarchy in order to separate the different models. Can anybody suggest a way forward?