I think that's a WAD (works as designed) The essence of a redirect is that send the message unaltered to somebody else. The received headers etc will remain unchanged, when you edit the message you're no longer redirecting it.

However, there is a workaround, save it as draft, go to the outbox open the message and edit it. When you view the headers you'll see that all headers added by mail servers have been removed after editing and also that the message has a new Message-ID.

A redirect is sending an identical message to another recipient, generally messages created by somebody else. As soon as you're editing it, you're falsifying messages with somebody else' name in the from header. I  think it's good for TB that it doesn't let you do that without you being aware that that isn't a normal redirect behaviour.

That should be posible with forwarding.
TB has two ways of forwarding: mime forwarding, that appears to be your default forwarding style. So you could try 'alternative forward'. If that does what you want you can switch the default forwarding method, by unchecking the bottom option for the forward template.
That's an account property, so you'll need to do that for every account.