So, I've taken the refurbed pipe die apart, and found...
That it has the "wrong" cutting teeth in it. In actuality, the teeth are just fine, they just don't seem to be the right teeth for for this particular die head. I can tell you they fit so tightly in their slots it's impossible to adjust them. I've looked at several different videos on replacing the teeth and setting up these dies, and they all show them moving freely until you lock them down by tightening the screws that hold the die together. I had to very carefully knock these out with a hammer and punch after I had the die apart. I can't imagine that's right.
It's also not good that they're for "National Pipe Straight Mechanical" (NPSM) rather than the "National Pipe Taper" (NPT) threads that pipe fitting use, so that probably won't help matters when it comes to assembly time for the piece I already have already threaded.
I feel like Marvin the Martian--"Delays, delays." The $30 replacement teeth should be here Friday. It would be cheaper if I just went back to work.