Yeah, you'd clamp from say the external and do all the internal chamfers then clamp from inside to do the external. Moving a couple of bolts and clamps is measured in seconds, compared to chucking up and adjusting your probe if you're finding need for it. And it reduces or entirely negates the chances of twisting your piece. You might also find that you're taking so much meat out of the part in the first op that the vice is distorting the work anyway once it's cut down so much.

Just a suggestion anyway and something to think about.