Cast Boxed Object back to Original Type

I expect there's one of two answers to this, either impossible or extremely simple and I've overlooked the obvious Google query.

The underlying issue is that I have a generic object being passed in via an EventHandler that boxes the object and obfuscates the true type; only at runtime do I know what the object is.

Admittedly the dynamic keyword can get around the issue, but I'd like to not lose IntelliSense and everything if I can avoid it. Plus, it doesn't solve not knowing what each of the properties of the generic object are without massive amounts of reflection.

EDIT: The idea is to be able to determine the true type of the an object in a method parameter, and then cast that object as it's true type without knowing it in advance. This is but a simplified example. Boxed may have been the wrong term.

An example:

public class Program
{
    static void Main(string[] args)
    {
        var container = new Container<Containee>(
            new Containee
            {
                Property1 = Guid.NewGuid(),
                Property2 = "I'm a property!",
                Property3 = DateTime.Now
            }
        );

        var boxed = (object)container;

        var originalType = boxed.GetType();

        // DOES NOT COMPILE: would like an operation like this
        // EDIT: Request for more detail
        var actualType = boxed as originalType;
        actualType.Entity.Property2 = "But I like this better.";
    }
}

public class Containee
{
    public Guid Property1 { get; set; } 
    public string Property2 { get; set; }
    public DateTime Property3 { get; set; }
}

public class Container<T>
{
    public Container(T entity)
    {
        Entity = entity;
    }

    public T Entity { get; internal set; }
}

Clearly that won't compile, as there's not really a way to cast as a variable. However, I'm hoping there's a way to get a reference to the actual