Yeah, I never would have guessed that a military 98 wouldn't feed the round it was designed for! You might try a 7x57 round in yours just to see. It might have had some work done to it to feed the .243.
There are a quite a few competent gunsmiths who can test your 98 for possible heat-treating. When I was fooling around with military 98's a lot I used the late Dave Gentry, who knew about as much about 98's as anybody around, but there are others. You might try Dennis Olsen in Plains, Montana.