You could try grinding up a HSS toolbit (say 6 – 8 mm sq ) to make a knife tool.
Mount it in the toolpost along the axis of the lathe, with 12 -15 mm protrusion
(Check that it will not hit the vice jaws! )
Having made a central hole with a drill, or drills at least as big as the toolbit proceed to take a series of cuts along the axis of the lathe.
The tool should be be more rigid than a long boring bar, and so should withstand deeper cuts, say 0.5 – 0.6 mm ,to rough out the bore. The boring tool can then be used to finish the bore, and to face the innner end.
Howard