I thought about shrinkage and as a (probably unnecessary) precaution I heated the steel tube to red before pouring in the lead. This gave scope for the tube to contract onto the lead. I never attempted to measure if it did but there has never been any sign of a loose core and I must have made three 55+ years ago. I did think of trying to "tin" the inside but it worked without it and it did not seem an easy thing to do. In any case I am not so sure that a loose core would be detrimental.
I once tried something just for fun without intention of using it for real. I fixed a relatively small diameter rod to the back end of a boring bar with a mass that could be moved back and forth. This was an harmonic damper and it could be tuned to stop chatter. It was great but I considered it too much hassle to use as a workshop device. I wonder if the bar in the video works on a similar principle but inverted and put up inside instead of dangling out the back like mine.

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