With the .243, you already seem to have most of your existing shooting covered...
As you pointed out previously, if you wanted to shoot 100grs, you could do that with the .243, which also covers all the bullet weights down to 55grs!
Therefore, seems to me , as you have a full-length M98 action to play with, you should start looking at cartridges with 57mm or 63mm cases, and that start about where the 6mms leave off in bullet weight. To me, that disqualifies the .25s, as not offering enough advance over the .243!
I think good options begin with the 6.5/06 (and AI) and .270Win...
Then the 7x57 (and AI), .280 (and AI) and finally the 30/06(and AI).
Considering the likelihood of you using it, other than on targets, the .338/06 and 35 Whelen are probably not going to do much for you.
The only other I'd suggest, if you want an Elk rifle, is running a 30/06 reamer into the existing 8mm barrel, if you still have it, for an 8mm/06...this would be your quickest and cheapest option too, of course!
Good luck with it,
Ed