The British Stainless Steel Association has a pretty good website. Seems that 303 is a slightly easier cutting version of 304 due to the addition of sulphur.
Although you can get through-hardening stainless steels (eg 420), most stainless steels don't contain carbon, so any hardening has to be surface treatments such as carburising, nitriding, chromising etc. Funny this should come, up as I discovered yesterday that a bearing part we had designed for through hardening had somehow been changed from 420 to 304L (the L denotes an almost total absence of carbon), rendering it only suitable for surface hardening. Not much use for a bearing, then.
Sounds as if you could machine it down. If the work hardening becomes an issue, you could anneal it as suggested.
Murray
Edited By Muzzer on 14/05/2016 19:56:04