Many thanks for comments.
@Rainbows – I like this method – If consistent readings are secured I will stick to it.
@JasonB – I think, too much is left to chance here
@ John Hinkley – no centers. Leadscrew is rolled. Anyway, I would need to extend bedways in any case.
@Hopper – I do have 4 jaw. I do not have Grip True. It is still not easy to center an awkward object in 4 jaw – hence my querry.
@ John MC & Martin Kyte – Method of production *is* known. It is rolled precision leadscrew ex McMaster Carr, 45-50 HRc hard, It has nice deep brown to black shiny finish on its surface. Do not know about any possible surface hardening. It is made of 4140 Alloy Steel and Mc Master Carr catalogue No is 98940A733. Do you have any ideas, how to approach the issue with this information? For example how *rolling* of the screw affect any possible irregularities? I would really appreciate any further ideas here.
I would really like to center it well – It will be a leadscrew in my lathe after all and needs to be kind for end bearings and clasp nuts.
Martin