I don't think I've gotten a straight hawken tang yet, so the first thing I do after I establish the top wrist profile is to straighten it out and file it so it's symmetrical. Then I bend it to match the profile of the wrist. I also smooth out the sides and make sure there is a consistent draft all around. Tangs, like any cast part, usually come pretty rough and need some refining, including un-twisting them.
One thing I never do is bend a tang cold. It's so much easier if you use heat, and you can pinpoint your bends. Banging a cold tang to straighten it out lacks control, and it would be really difficult to un-twist it without heat. Hitting the cold metal can also booger up the edges.
You can straighten out your tang if you use heat and a logical systematic approach. I suggest you first heat it and get the twist out. then find the center and straighten it out sideways, then file for symmetricity, then bend for the wrist profile.
As far as the mortice being too loose, try the spread-by-hammering technique mentioned by others. I have used this method on small parts, but never an entire part like a tang. It should work though, again, just take a systematic approach. Good luck. Bill