Those $400 presses have chuck that will close down to nothing. Buying a good chuck ain't cheap.... and when you do you'd better know what taper the press spindle is... if you can the old one off. If it's threaded you're "threaded".
That's why the chuck I recommended costs as much as the press. It too closes down to 0", and adds the convenience of keyless operation. Of course, I wouldnt expect the press to have the accuracy of the $400 model, but now we have options ranging from $100 to $400+ for the buyer to choose from.