Hi Mark,
Given the size of the material you are turning it’s unlikely that the material is exhibiting any form of stress release. That said if the skin of any material exhibits a relative hardness then the initial cuts can sometimes produce the effect you are getting but should be long gone by the time you get to the finished size you quote. ‘Black’ hot rolled bar is not very round at its best so is usually skimmed before final turning.
Normally though, if something turns out of round it’s usually a, the tool or b, the work ‘moving’ in or out relative to each other. If the headstock and tailstock are ‘sound’ then it may be caused by the cross slide and/or the top slide gibs needing a nip up. The run out of 03 is quite small so movement wouldn’t need to be much.
There are other factors that can come into play also – a faulty tailstock live centre – though this normally would produce a tapering effect down the length of the work – and/or worn jaws or scroll in the chuck. Is this 03 run out consistant down the length of the reduced diameter?
If the .03 run out is still there after a final .05 cut – take two passes at the same setting – then you probably have to look at the set up. Start with the chuck as movement of the tool is unlikely with such a small depth of cut.
Hope this gives you some idea from where to start to look
Regards – Ramon