Maybe send it off to JES and have it rebored to .35, and save the .358 barrel blank for another project? A .35-303 would be interesting and surely the old girl would accommodate it. A JES rebore is very affordable, but then there's the issue of custom dies. Just how much money do you wish to throw at a 100 year old No.1 MkIII? On the other hand it would save having to profile the new barrel to fit the stock.
I like building unique firearms from older rifles that are fubar, such as my 6.5x55 Arisaka and 6.5x57 Gewehr 88/05. I'm mostly considering the .358" bore because A) if I don't have to buy a barrel, I can put more towards other aspects like the machine work and making better wood for it than the butchered military wood on the rifle, B) I want something between my 450 Bush and the various .30 cal rifles I own, and C) I'd like to keep the ammunition costs (including dies) down a little if I can, which is part of why I figured Id ask if there were any decent chamberings this community could think of that werent wildcats like most the ones I'm currently debating.
I'm not opposed to a rebore per say, but a buddy wants to use the barrel for a 7.62x39 carcano and offered enough that I'm not too concerned about trying to have it rebored if I can get the barrel off.