I can't give any information for annealing, but I did have a similar problem with my 70 year old Atlas lathe tailstock barrel which was badly pitted and not made of hardened steel.
The original barrel was 1&1/8th inch diameter and I couldn't find an equivalent sized barrel apart from second hand ones which were probably in the same condition as the one I had.
There were straight shank MT2 inner to MT3 outer adapters which had an outer dia of 1 1/4" and I thought of trying annealing it and having a go at machining, The plan was I would cut the MT3 end off and and after annealing and machining to the smaller diameter, fit the part of the old barrel with its acme screw thread to the new MT2 straight sided shank. In the end I didn't anneal it.
Pic below shows the end cut off the hardened steel new part and the badly pitted old tailstock barrel with its acme screw part also cut off.

After much deliberation I decided to grind the outer surface of the new straight sided MT2 shank, I only needed to grind off 1/16" radially, and I fitted a modified chain saw grinder in the toolpost for the job.
The job went quite well and I finished it by lapping with diamond paste, I found that the inside of the new part was not as hard as the outer surface and the finish was just as good as the originally purchased item.
Below….the new tailstock barrel fitted…. it works great and I set it true to the lathe axis using a dti method, it is absolutely spot on. As the barrel was now looking good I fitted a digital readout and partly embedded it in the tailstock casing so it didn't stick out so much.

I know it's not exactly what you were asking but other ideas are sometimes useful.
…Bob…