Smokey: I'm not so sure it will handle that fat cartridge that easily. I think the length is not an issue but the fat case is. Although it may not be. The M48/48A is a medium length Mauser action - in that regard the length of the 350 Rem may not be the issue. Pressures limits may be the real issue. The 8x57 is in the 45-48K pressure range - I'm not certain where the 350 Rem stands in this regard but if it is much higher I might tend to avoid the conversion unless I spoke with a gunsmith who knows the M48/48A action and the working pressures of the 350 Rem.
There was some talk on the Mil-surp forum about using 308 Winchester hunting ammo in a Chilean Mauser converted from 7mm to 7.62x51 Nato. The concern was that the military NATO round was in the same pressure ranges as the original 7mm Mauser (45-48K) but the 308 pressure ranges went well into the 50+K range and even as high as 62K and that the Mauser action, being older, might not be able to handle those pressures. I think your Yugo will definately handle the 358 but a question is: what do you want to do with this rifle that good quality 8mm hunting ammo won't do for you? Hope this helps. Mikey.