No problem machining 316SS - it's harder than mild steel
, but not all that much.
I was talking to the local Johnson pumps bloke who suggested using a duplex stainless (much harder and more corrosion-resistant than the standard 316 shafts). Now that might be a challenge to turn on a lathe with normal tool steel. Anywway, the old shaft has lasted many years until now, and the engine
is not a pup by any means, so I reckon 316 would see it out.
By the way, Johnson have pumps which look surprisingly similar to the Yanmar one (guess who makes them for Yanmar!). The one in question is listed for less than $300 at pumpvendor.com, so I'll check it's dimensions and if it fits, I might go that way.