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I think I'd just use the bandsaw to get it close
To me it was being held by the wrong end, rather than hold the short bit of 5/8" that you wanted you should have held it by the remaining 5/8" stock and just parted off the bit you wanted. That way you have the full length of the chuck jaws in contact with the work not less than 1/4"5/8" I would be parting at 5-600rpm and using power feed and a little coolant, but a syou are starting out handfeed will give you teh feel of what can and can't be done but use two hands on te hrim of the handwheel so you can get a constant feed.
At least I learned how much difference a thousandth makes