While a single entity can have multiple identifiers, one is usually canonical in a communication environment. For example, we say "Istanbul was founded in the 7th century BC" when speaking of the present-day city, But we say "Byzantium was founded" when we wish to limit the discussion to the pre-Constantine era. If we wish to span multiple eras, Istanbul is the only choice, as that is the canonical identifier.
As such, I believe you should refer to Manning as Chelsea if she is the subject, but may refer to her as Bradley if the leak is the subject. It would be helpful to qualify her name as "Chelsea Manning, who was at the time known as Bradley", "Bradley Manning, who later changed her name to Chelsea", or some similar construction for audiences who are not well aware of her, to help them connect historical knowledge to your topic.
This is perfectly sensible, and exactly what I was looking for. It chooses the most relevant and least confusing identifier for the context it was used in. The question then becomes, "Is this acceptable to the transgender community?" and "Is this in common use?"
As such, I believe you should refer to Manning as Chelsea if she is the subject, but may refer to her as Bradley if the leak is the subject. It would be helpful to qualify her name as "Chelsea Manning, who was at the time known as Bradley", "Bradley Manning, who later changed her name to Chelsea", or some similar construction for audiences who are not well aware of her, to help them connect historical knowledge to your topic.