When you're glaze breaking for a re-ring , you're really not trying to " straighten out" the cylinder walls ,I M O . For an at home re--ring , the dingle balls seem to do just fine . If you're building high performance race motors, there are better ways .I don’t like nor recommend ball hones for what I think are good technical reasons. That said the hone used depends on the rings used. I think they are marginally OK if you have straight walls. If this engine has wall taper, out of round or wavy walls the ball hone is incapable of correcting these conditions. Being flexible in all dimensions they fake you you out leaving a great looking finish but all they do is put a shine on whatever surface is there they don’t correct defects, so you need to appreciate that going in.
Chrome and plain cast iron use a coarse hone as in 240.
Moly prefers a finer finish from a less coarse hone as in 320.
Some guys prefer what’s called a plateau finish where you start with a coarse hone and finish with a finer grit.