Thanks Stephen. I had those thoughts about using more leverage on the chuck, but allowed discretion to be the better part of valor and refused to use any more pressure than I could muster with my bare hand. In the end it was enough.
I'm convinced that the Brownells bit I was using could be easily broken with more leverage. I'll try new things, but I'm very cautious. I can picture a line that can be easily crossed where the leverage exceeds the tensile strength of the bit.
I was using a bolted down vise to hold the action. But, thanks again for the helpful advice. It is always very much appreciated.