Yes the chuck should be padded with something and I am thinking I will make some brass pads.
Also, the diameter of the barrel at the spot where it passes out of the back throat of the spindle is slightly smaller than the diameter of the throat. So I will need something to shim the barrel there.
I have some rubber sheet stock but I have never tried that and I am afraid the barrel will not be held secure enough in the chuck.
My reading of history convinces me that most bad government results from too much government. Thomas Jefferson