Since the bolt you have from another frame has the same thread, it should be possible to find another bolt with a shorter shoulder, which should then be able to get tight. To confirm this, get a few more washers the same size as what you have and put them on the bolt side and see if the clamp closes without a seatpost - this confirms what is going on. The washers cause the bolt shoulder to be held further away from the nut (that you cannot remove), so you should be able to tighten the seatpost clamp. Adding washers is the easiest way to address the challenge, and presents no risk to what you have regardless of the cause of the problem.

I agree that finding a way to remove the nut makes sense, but it should not be necessary, as the way it is stuck is not the cause of your problem - it may be too long for this clamp (so ideally it should be replaced with one that fits the clamp), but I cannot see how it could be too far into the socket, because it should be all the way in when working correctly.

-Will