In the WWI period, Remington and Westinghouse contracted with Russia to make Model 1891's in the U.S. Many thousands were not delivered due to the revolution in Russia; to fill a need (and to bail out the companies), the U.S. bought them and used them as training rifles in WWI. When they were sold on the market, several companies converted them to .30-'06, and the major ammo companies also made the 7.62 Russian cartridge. The father of a good friend used one in .30-'06 for deer hunting for years and usually got his deer.
There were many scare stories later, and assorted rumors, but I do not know of any conversions actually blowing up or coming apart. AFAIK, the barrels were set back and rechambered. As for the bore/groove diameter, it was generally believed that it was the same as .30-'06, but no one seemed to care much, since the rifles were all of $2.50 or something like that. I have not seen a conversion for years, and simply don't remember any details, but they seemed to work OK.
Jim