Why do you need to anneal for machining? We actually prefer strain hardened stainless for machining, as we get less stringy chips, better surface finish, and reduced tearing (with form tools). For some of our machined products, we actually specify fairly strongly strain hardened barstock and anneal following machining, as we need the reduced mechanical properties of the annealed stainless for product performance.
It's important that you source barstock specified for machining, also. Such barstock will have about 0.025% sulfur and about 0.035% phosphorous, which will aid machinability, although at a slight loss of corrosion resistance.