I have done a fair bit of machining on 316L usually custom gate pins for rowing boats i used to build, I found that sharp HSS tools with plenty of synthetic oil coolant gave great results with a good finish. Havent had the need for carbide yet! Work hardening usually happens when drilling too fast with not enough feed pressure.
As for galling stainless I had one set of rowlock pins i made from an unidentified grade lump of stainless bar that galled & seized in the socket first time out, this isnt even revolving just oscillating back & forth about 45degrees with a bloke pulling an oar! I had to scrap them & make new ones.