However he seems to have a different interpretation of “soft jaws” use. He is using them simply as a softer surface to protect his work when most refer to soft jaws as ones that are not hardened and can therefore be machined in situ for both ensuring the work is concentric and if thin then without wobble.
But I suppose if he has put that much work into his protective jaws he would be reluctant to start chopping them up.
If you held a few narrow parts in those the soft copper would soon start to deform and you would end up with ridges and the chance of bellmouthing but Ok for holding full length assuming they ran true.