I think its plenty doable, though the action is a bit short for the 30-06.
People shoot .308 ( a higher pressurecartridge than the 30-06)through spanish mauser 95s which are made with far inferior metallurgy than the Swedish and German 96s (the german 96s were all made of Swedish steel)
Plenty of german made m93 mausers have been rechambered for 8x57 for Turkey- the 8x57 has about the same pressure rating as the 30-06.

A mauser 98 is a bit beefier- it has a slightly thicker receiver at the ring, but once again, m96s were made with superior steel than a lot of them- especially yugoslavian and spanish mauser 98s.

The third safety lug doesn't really do anything.Its a nice thought, but if you have a bolt that is so brittle that the large locking lugs shear off, that much smaller safety lug isn't going to do much. The real big improvements in the mauser 98 has to do with the gas handling- mauser 96s vent gasses into the magazine well, while mauser 98s vent it out of the side of the receiver and have a gas shield on the bolt shroud to channel debris and gasse away from the face. Most modern rifles have neither safety lugs nor gas shields. The last and probably most drastic improvement of the mauser 98 is the cocking on openeing of the bolt- it takes a lot more design consideration and machining to make a rifle that cocks on opening than rifles that cock on closing.

I've seen pictures of the aftermath of some bozo who took up reloading and figured that if a powder is safe for pistols that it should be safe for rifles too. He filled 6.5x55 cases to theneck with bullseye. Predictably, the first round fired destroyed his rifle. The action was twisted, the bolt was sprung upward (once again , a safety lug wouldn't have done much) and the stock was shattered around the magazine well from the gasses venting. The shooter walked away with minor cuts to his handsand forearms.