I am seriously thinking about picking up a Schmidt-Rubin K31 in 7.55 Swiss. These rounds are expensice to shoot, can these rifles be rechambered to a .308?
Not easily. The head size on the 7.5 Swiss is quite a bit larger than the .308.
In fact the whole case is a little larger than the .308, so it would probably be a rebarrel situation. Even then, the boltface and extractor wouldn't be a good fit.
A better solution would be to reload for it. Boxer primed brass is available and it uses .308 bullets.
Well actually, mine is a 1911 model, but the armory eventually rebarreled a good many of each of the K31 and 1911's. It wasn't a hard fit for the extractor and the bolt face are basically the same. You could have yours converted by a smith that knows what he is doing very easily or you can buy in volume for the original caliber when it goes on sale.