Running the tool a number of times to take out the "spring " seems to be a model practice ,not used in full size practise, looking at the photo I would reduce the length of bar protruding from the tool post so that the tool only just can protrude from the back end of the bore,to make the tool more rigid. The only real advantage of reaming is it should provide a parallel bore which could be necessary if the lathe is worn and turns taper. Keep the rad on the tool tip to a minimum ,just enough to give the required finish ,too big a rad can induce chatter.As for speed I would use between 100 and 200 rpm,depends on how well its balanced,go too fast and the tool will wear,go too slow and no harm will be done and the tool edge lasts a long time.Honing will produce a nice bore,use lubricant 50/50 light oil and white spirit,works well on the hot air engines I have made.