If you have a Dremel or other hand held rotary type tool,,or a drill,,or a drill press,,,place one of the grinding stones available that you can just chuck in place.
Use a rough cutting stone. They cut cooler and faster. Not interested in looks. Just making the die(s) more usable.
Then free hand, or with the assistance of the drill press holding the bit for you,,grind the center portion of the die out so your 'to be threaded' stock can reach the die's teeth and thread all the way down.
It won't be pretty in many instances as most Dremel work is not! But it'll make quick work of it with a rough cut stone and get the excess material gone for you and the die usable for your needs.